Answer:
When a passenger is sitting in a stationary bus it is under the law of inertia of rest that is the body resists any change in its state of rest.
Explanation:
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Can u please help with first two tasks
Workbook:complete physics for Cambridge secondary first
Electromagnetic induction is a phenomenon in physics that occurs when a varying magnetic field produces an electric current or voltage in a conductor. It was first discovered by Michael Faraday in the early 19th century and is now a fundamental principle of modern electrical technology.
When a conductor, such as a wire, is moved through a magnetic field, or when the magnetic field itself changes, a voltage is induced across the ends of the conductor. The magnitude of the induced voltage is proportional to the rate of change of the magnetic field and the number of turns of wire in the coil.
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What evidence have you discovered to explain how plants, such as sunflowers, and animals process energy?
Answer:
Living organisms collect the energy from the sun, and use water and carbon dioxide to produce sugars in the process known as photosynthesis. Animals can use the energy and sugars that have been provided by the plants. When plants get enough light, plants can make their own food
Plants process energy through photosynthesis, a process that converts light energy into chemical energy. Animals process their energy through cellular respiration, which turns biochemical energy from nutrients into adenosine triphosphate. These processes are interrelated, involving a cycle of oxygen, glucose, carbon dioxide, water and energy.
Explanation:Plants, such as sunflowers, and animals process energy differently. Photosynthesis is the process by which plants, including sunflowers, convert light energy, usually from the sun, into chemical energy that can be later released to fuel the organisms' activities. This process occurs in the chloroplasts, specifically using the chlorophyll in the leaves.
Animals, on the other hand, get their energy through cellular respiration, a set of metabolic reactions and processes that take place in the cells of organisms to convert biochemical energy from nutrients into adenosine triphosphate (ATP), and then release waste products. Unlike photosynthesis which occurs in the chloroplasts, cellular respiration mostly occurs in the mitochondria.
The two processes, although different, are interrelated. Plants produce oxygen and glucose (sugar) during photosynthesis, which are then used by animals (and plants as well) in cellular respiration to produce carbon dioxide, water and energy. Then the carbon dioxide and water are taken up by the plants to use in photosynthesis.
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A block of wood weighing 15 N rest on top of the table. How mush force is exerted by the table on the blockso that it will remainat rest. Explain your answer
What is Ceres?
The largest asteroid identified to date.
The asteroid closest in orbit to the Earth.
The comet that passes near Earth most often.
The meteor that probably killed the dinosaurs.
The Ceres is (a).The largest asteroid identified to date is correct option.
With a diameter of around 590 miles (940 km), Ceres is the biggest asteroid between Mars and Jupiter. It is regarded as a minor planet, like Pluto, and was found in 1801 by Giuseppe Piazzi. Ceres is made of rock and ice, and due to its low density, it is likely that it contains a substantial amount of water ice inside.
The NASA Dawn spacecraft visited Ceres in 2015 and orbited the dwarf planet for more than three years, gathering useful information and taking stunning pictures of it.
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URGENT 50 POINTS
Show all Steps of your work.
7. Mohammed whose mass is 50kg swings back and forth on a long vine makes an angle 45 from the vertical resting position. His friend Abdella notices in amazement that he makes 30 complete swings in 2.0 minuies.
(a) What is the frequency (in hertz) of Tarzan's swing?
(b) What is the period of oscillation?
(c) How long is the vine he is using?
(d) Calculate the Restoring force on Mohammed?
The frequency of oscillation of the swing is 0.25 Hz.
The time period of oscillation of the swing is 4 s.
The length of the vine of the swing is 3.97 m.
The restoring force acting on Mohammed is 692.9 N.
Mass of Mohammed, m = 50 kg
Angle made by the vine with the vertical, θ = 45°
Number of complete swings made by Mohammed, n = 30
Time taken for this swing, t = 2 minutes = 120 seconds
a) The frequency of the swing is defined as the number of complete oscillations in one second.
So, the frequency of oscillation of the swing is,
f = n/t
f = 30/120
f = 0.25 Hz
b) The time period of oscillation of the swing is,
T = 1/f
T = 1/0.25
T = 4 s
c) The expression for the time period is given by,
T = 2π√(l/g)
T² = 4π² x (l/g)
l/g = T²/4π²
Therefore, the length of the vine of the swing is,
l = T²g/4π²
l = 4² x 9.8/4 x (3.14)²
l = 3.97 m
d) The restoring force acting on Mohammed,
F = mg sinθ
F = 50 x 9.8 x sin 45°
F = 490 x 1/√2 = 490/1.414
F = 692.9 N
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b) An iron block of mass 4kg rest on an aluminium platform. A horizontal force of 20N is applied to the block. The coefficient of limiting friction between the two surfaces is 0.6. i) Will the block move? ii) If it moves, what will be its acceleration.
The block won't move since the applied force of 20 N is less than the maximum frictional force of 23.52 N.
How can I calculate the friction force between the blocks at its maximum?When an object is on a rough surface, friction is a force that acts in the opposite direction from the direction of motion. FMAX=R F MAX = R where is the coefficient of friction and R is the normal reaction between the two surfaces is the maximum or limiting value of friction between two surfaces.
[tex]F_gravity = m * g[/tex]
[tex]F_norm = F_gravity = m * g = 4 kg * 9.8 m/s^2 = 39.2 N[/tex]
[tex]F_friction = 0.6 * 39.2 N = 23.52 N[/tex]
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A 0.120 kg, 90.0-cm-long uniform bar has a small 0.055 kg mass glued to its left end and a small 0.110 kg mass glued to the other end. The two small masses can each be treated as point masses. You want to balance this system horizontally on a fulcrum placed just under its center of gravity.
How far from the left end should the fulcrum be placed?
The fulcrum should be placed 0.120 m from the left end of the bar to balance the system horizontally.
What is balance?
To balance the system horizontally, the center of gravity (CG) of the bar and the attached masses should be placed directly above the fulcrum. We can find the location of the CG using the following formula:
CG = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
where m1, m2, and m3 are the masses of the bar, the 0.055 kg mass, and the 0.110 kg mass, respectively, and x1, x2, and x3 are their respective distances from the left end of the bar.
We know that the total mass of the system is:
m = m1 + m2 + m3 = 0.120 kg + 0.055 kg + 0.110 kg = 0.285 kg
Let x be the distance from the left end of the bar to the fulcrum. Then, the distance from the fulcrum to the center of gravity is (L/2 - x), where L is the total length of the bar (90.0 cm). Therefore, we want to find x such that:
CG = (L/2 - x)
Substituting the expressions for the CG and the masses, we get:
(m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) = (L/2 - x)
Simplifying and rearranging, we get:
x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) - L/2
We can choose any two points on the bar as reference points, and take their distances as x1 and x3. Let's choose the left end of the bar as x1 = 0, and the right end of the bar as x3 = L = 90.0 cm = 0.900 m. Then, we can find x2, the distance from the left end to the 0.110 kg mass, as:
x2 = L - x1 - x3 = 0.900 m - 0 m - 0.090 m = 0.810 m
Substituting the masses and distances, we get:
x = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3) - L/2
x = (0 kg × 0 m + 0.055 kg × 0.810 m + 0.110 kg × 0.900 m) / (0.120 kg + 0.055 kg + 0.110 kg) - 0.450 m
x = 0.570 m - 0.450 m
x = 0.120 m
Therefore, the fulcrum should be placed 0.120 m from the left end of the bar to balance the system horizontally.
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The 4.00 kg block is attached to a vertical rod by means of two strings. When the system rotates about the axis of the rod, the strings are extended as shown in the (Figure 1) and the tension in the upper string is 78.0 N. Find the number of revolutions per minute at which the lower cord just goes slack.?
The number of revolutions per minute at which the lower cord just goes slack is approximately 38.2 rpm.
To solve this problem, we need to use the concept of centripetal force and tension in the strings. When the lower string just goes slack, the tension in the string is zero and the centripetal force required for circular motion is provided only by the weight of the block.
We can start by calculating the weight of the block using the formula:
[tex]F_g[/tex] = m * g
Where [tex]F_g[/tex] is the weight, m is the mass, and g is the acceleration due to gravity. Substituting the given values, we get:
[tex]F_g[/tex] = (4.00 kg) * (9.81 m/s²) = 39.24 N
Since the tension in the upper string is 78.0 N, the net force acting on the block is:
[tex]F_{net}[/tex] = T - [tex]F_g[/tex] = 78.0 N - 39.24 N = 38.76 N
This net force provides the centripetal force required for circular motion, given by the formula:
[tex]F_{cp}[/tex] = m * v² / r
Where [tex]F_{cp}[/tex] is the centripetal force, m is the mass, v is the velocity, and r is the radius of rotation. Since we are asked to find the number of revolutions per minute, we can convert this to radians per second using the conversion factor:
1 revolution = 2π radians
1 minute = 60 seconds
Substituting the given values, we get:
Fcp = (4.00 kg) * v² / r
38.76 N = (4.00 kg) * v² / r
Solving for v²/r, we get:
v² / r = 38.76 N / 4.00 kg
v² / r = 9.69 m/s²
Next, we can use the fact that the length of the upper string is twice the length of the lower string to find the radius of rotation:
2l + l = 3l = r
Where l is the length of the lower string. Substituting the given values, we get:
3l = r = 0.600 m
Finally, we can substitute this value into the equation for v²/r to get:
v² / (0.600 m) = 9.69 m/s²
v² = 5.814 m²/s²
v = 2.41 m/s
To convert this to radians per second, we multiply by 2π and divide by the circumference of the circle:
ω = 2πv / (2πr) = v / r = 2.41 m/s / 0.600 m = 4.02 rad/s
To find the number of revolutions per minute, we can multiply this by the conversion factor:
1 radian per second = 60 / 2π revolutions per minute
N = (4.02 rad/s) * (60 / 2π) = 38.2 rpm
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By how much do you stretch your 0.600-cm diameter nylon rope when you hang 23.0m
below a rock outcropping. Assume your mass is 75.0 kg and your nylon rope has Young’s modulus of 5.00 × 10^9 N/m^2.
Answer:
To solve for the amount of stretch in the nylon rope, we can use the equation for the elongation (stretch) of a rope under tension:
ΔL = FL / AE
where ΔL is the change in length of the rope, F is the force on the rope, L is the original length of the rope, A is the cross-sectional area of the rope, and E is the Young's modulus of the rope.
First, we need to find the force on the rope. This is equal to the weight of you and the rope:
F = mg = (75.0 kg + mass of rope)g
Next, we need to find the cross-sectional area of the rope. The diameter of the rope is given as 0.600 cm, so the radius is 0.300 cm = 0.00300 m. Therefore, the cross-sectional area is:
A = πr^2 = 2.83 × 10^-6 m^2
Now we can plug in the given values and solve for ΔL:
ΔL = FL / AE = [(75.0 kg + mass of rope)g](23.0 m) / [(2.83 × 10^-6 m^2)(5.00 × 10^9 N/m^2)]
We can simplify this expression by using the fact that the mass of the rope is much smaller than your mass, so we can assume that the force on the rope is equal to your weight:
ΔL = (mg)(23.0 m) / (A E) = (75.0 kg)(9.81 m/s^2)(23.0 m) / [(2.83 × 10^-6 m^2)(5.00 × 10^9 N/m^2)]
Solving for ΔL, we get:
ΔL = 0.068 cm
Therefore, the nylon rope stretches by approximately 0.068 cm when you hang 23.0 m below a rock outcropping.
If the adhesive force between solid molecules and liquid molecules is relatively weak, the phenomenon of non infiltration will be formed. True or false?
If the adhesive force between solid molecules and liquid molecules is relatively weak, the phenomenon of non infiltration will not be formed. False.
What is non-infiltration about?If the adhesive force between solid molecules and liquid molecules is relatively weak, the phenomenon of infiltration (or wetting) will be formed, as the liquid will spread out over the surface of the solid.
Non-infiltration is a phenomenon where a liquid is unable to wet or spread over the surface of a solid due to the strong adhesive force between the solid and liquid molecules. Instead of spreading out, the liquid will form droplets on the surface of the solid.
Non-infiltration is the opposite of infiltration (or wetting), where a liquid is able to spread over the surface of a solid due to a weak adhesive force.
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HELPPPPP MEEEEEEE. genes can __________ many traits and can be ____________ through biotechnology
Genes can shape many traits and can be modified through biotechnology.
What are genetic engineering techniques?The expression genetic engineering techniques refer to all procedures that use recombinant DNA to create or redesign gene sequences, which invariably may modify or change the expression of a given phenotypic feature in the target organism in which this sequence is being inserted.
Therefore, with this data, we can see that genetic engineering techniques can modify a phenotype to express a desirable trait such as by inserting the insulin gene into bacteria.
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Explain why sound wave travel faster in liquids than in gases
Answer:
Sound travels faster in liquids than in gases because molecules are more tightly packed. In fresh water, sound waves travel at 1,482 meters per second (about 3,315 mph). That's well over 4 times faster than in air!
Explanation:
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A concave mirror is designed so that an object 1.0 m in
front of it produces a real image at a distance of 1.6 m in
front of the mirror. What is the radius of curvature of the
mirror?
Answer:
We can use the mirror equation to find the radius of curvature of the mirror.
The mirror equation is:
1/f = 1/d₀ + 1/dᵢ
where f is the focal length of the mirror, d₀ is the object distance, and dᵢ is the image distance.
In this problem, we are given:
d₀ = 1.0 m
dᵢ = 1.6 m
We need to find f, and then we can use the relationship between f and the radius of curvature R to find R.
From the mirror equation, we can rearrange to solve for f:
1/f = 1/d₀ + 1/dᵢ
1/f = 1/1.0 + 1/1.6
1/f = 1.6/1.0 * 1/2.6
f = 0.615 m
Now, we can use the relationship between f and R to find R:
f = R/2
R = 2f = 2 * 0.615 m = 1.23 m
Therefore, the radius of curvature of the concave mirror is 1.23 m.
4. Define the terms; I. Frequency II. Wavelength III. Velocity as applied to a periodic wave motion. State the relationship between them. b) Two turning forks have frequencies of 200Hz and 300Hz. Calculate the difference in the wavelengths of the notes they emit. [Speed of sound in air = 330ms-¹]
Answer:
Wavelength : It is defined as the distance travelled by a wave during the time a particle of the medium completes one vibration. It is denoted by k. Its SI unit is metre. Frequency: It is the number of occurrences of a repeating event per unit of time. Its SI unit is Hertz (Hz).
Explanation:
When does a force do maximum work
Answer:
when the angle between the displacement and direction of force is zero
Answer:
Only when the force is applied in the same direction as the displacement of the object on which it acts, it does maximum work. This is because the work done by a force is given by the dot product of the force and displacement vectors. The dot product of two vectors is maximum when they are parallel to each other. Therefore, when a force is applied in the direction of displacement, it does maximum work.
When a force is applied perpendicular to the displacement, it does no work at all. This is because the dot product of two perpendicular vectors is zero. When a force is applied at an angle to the displacement, it does some work but not maximum.
It's important to note that the amount of work done by a force also depends on its magnitude and the distance over which it acts. The greater the magnitude of the force and the longer the distance over which it acts, the more work it will do.
In summary, a force does maximum work only when it is applied in the same direction as the displacement of the object on which it acts.
of the following stars, which one has a mass less than that of our sun? The choices are Sirius B, Altair, Arcturus, Spica, and Rigel.
Answer:
Sirius BExplanation:
Here we go !!!!
Sirius B: A white dwarf star and companion to Sirius A, the brightest star in the sky. It has a mass of only about 0.98 times that of the sun, making it less massive than our sun.Arcturus: A red giant star located in the constellation Boötes, with a mass of about 1.1 times that of the sun.Spica: A binary star system composed of two hot, blue stars located in the constellation Virgo. The primary star has a mass of about 11 times that of the sun.Rigel: A blue supergiant star located in the constellation Orion, with a mass of about 17 times that of the sun. It is one of the brightest stars in the sky and is a part of Orion's Belt.Altair: A main-sequence star of spectral type A7V, located in the constellation Aquila. It has a mass of about 1.8 times that of the sun, which means it is more massive than the sun.I hope this information helps!
why does widening the prism cause the beam to bend more?
Widening the prism adds additional glass, which slows light down even further and increases the amount of refraction.
Is a prism reflective or flexible?The angles and plane sides of a prism cause light to be bent, or refracted, when it flows through them; the degree of refractive distortion varies somewhat depending on the wavelength of light.
When light travels from the air to the prism's glass, its speed changes, causing the light to bend and shift course. Once light enters the prism, it bends because the refraction indices of the air and glass differ. The light exits the prism bent even more since the sides are slanted.
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How much more force can the larger piston exert compared with the force applied to the smaller piston
Katie, a 60 kg person, stands at the edge of a well and holds a rope attached to an 8 kg bucket of water resting in the water below. With her first tug up on the rope, the bucket speeds up to 3 m/s while it rises 0.9 m. What is the bucket’s acceleration? How quickly is Katie accelerating? How hard is Katie pulling on the bucket? What is the normal force on Katie?
To solve this problem, we can use the following equations:
F_net = ma (Newton's second law)
F_tension - F_gravity - F_buoyancy = ma (sum of forces on the bucket)
F_gravity - F_tension - F_normal = 0 (sum of forces on Katie)
where:
F_tension is the tension in the ropeF_gravity is the weight of the bucket and KatieF_buoyancy is the buoyant force on the bucketF_normal is the normal force on Katiea is the acceleration of the bucketFirst, we can find the tension in the rope:
F_net = ma
F_tension - F_gravity - F_buoyancy = ma
F_tension = ma + F_gravity + F_buoyancy
The weight of the bucket is:
F_gravity_bucket = m_bucket * g = 8 kg * 9.8 m/s^2 = 78.4 N
The weight of Katie is:
F_gravity_Katie = m_Katie * g = 60 kg * 9.8 m/s^2 = 588 N
The buoyant force on the bucket is equal to the weight of the water displaced by the bucket, which is:
F_buoyancy = m_water * g = m_bucket * g = 78.4 N
Substituting these values, we get:
F_tension = (m_bucket + m_Katie) * a + F_gravity_bucket + F_gravity_Katie + F_buoyancyF_tension = (8 kg + 60 kg) * a + 78.4 N + 588 N + 78.4 NF_tension = 68 a + 744.8 NNext, we can find the acceleration of the bucket:
We can use the kinematic equation:
v^2 = u^2 + 2as
where:
v is the final velocity (3 m/s)u is the initial velocity (0 m/s)s is the displacement (0.9 m)Solving for a, we get:
a = (v^2 - u^2) / 2sa = (3 m/s)^2 / (2 * 0.9 m)a = 5 m/s^2Therefore, the acceleration of the bucket is 5 m/s^2.
Next, we can find the tension in the rope:
F_tension = 68 a + 744.8 NF_tension = 68 * 5 m/s^2 + 744.8 NF_tension = 1075.6 NTherefore, Katie is pulling on the rope with a force of 1075.6 N.
Finally, we can find the normal force on Katie:
F_gravity_Katie - F_tension - F_normal = 0
F_normal = F_gravity_Katie - F_tension
F_normal = 588 N - 1075.6 N
F_normal = -487.6 N
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The critical angle for total internal re
ection at a liquid-air interface is
42.5.
(a) If a ray of light traveling in the liquid has an angle of incidence at the
interface of 35.0, what angle does the refracted ray in the air make
with the normal?
(b) If a ray of light traveling in air has an angle of incidence at the
interface of 35.0, what angle does the refracted ray in the liquid make
with the normal?
) Find mass and speed of 2 MeV electron
According to the equation E=(-1)mc2, where [tex]E=3.2 x 1013 J[/tex] and [tex]=1.0000037[/tex], a 2 MeV electron has a mass of [tex]9.11 x 1031 kg[/tex] and a speed of [tex]2.195 x 108 m/s.[/tex]
How are masses expressed in MeV?Additionally, as energy and mass are connected by Einstein's famous equation E = mc2, the masses of elementary particles are sometimes stated in electron volts as well. An electron, for instance, has a mass of 0.51 MeV/c2, where c is the speed of light.
What does 2 MeV proton mean?Moving perpendicular to a 2.5 T magnetic field is a 2 MeV proton. The proton is under a force of (1.6 10 27 kg of proton mass)
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A wave has a frequency of 11 Hz and a wavelength of 9 meters
what is the speed of the wave
The speed of the wave is 99 meters per second.
What is Wave?
A wave is a disturbance or variation that travels through a medium or space, transferring energy without the net movement of matter. Waves can occur in various forms, such as mechanical waves that require a medium for propagation (e.g., sound waves, water waves) or electromagnetic waves that can travel through a vacuum (e.g., light waves, radio waves).
The speed of a wave can be calculated using the formula:
speed (v) = frequency (f) x wavelength (λ)
Given that the frequency (f) is 11 Hz and the wavelength (λ) is 9 meters, we can plug these values into the formula to calculate the speed of the wave:
v = 11 Hz x 9 meters
v = 99 meters per second
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130% 00 1. A 345 g of copper is hanged on a spring wire of 30 cm in diameter as a result, the spring stretches from 75 cm to 80 cm. (8 marks)
1.1. What is the stress of the spring?
1.2 What is the strain of the spring?
1.3 What is the young's modulus of the spring?
1.4 Calculate the spring constant.
The center of gravity of a 5.00 kg irregular object is shown in (Figure 1). You need to move the center of gravity 1.60 cm to the left by gluing on a 1.50 kg mass, which will then be considered as part of the object.
Where should the center of gravity of this additional mass be located?
The moment of the weight of the 1.50 kg mass about the CG of the 5.00 kg object will be considered as part of the object.
The center of gravity of the additional 1.50 kg mass should be located 1.60 cm to the right of the current CG of the 5.00 kg object.
What is the moment ?
We can use the principle of moments to determine the location of the center of gravity of the additional 1.50 kg mass that needs to be glued on.
The principle of moments states that the sum of the moments of all the forces acting on an object is equal to the moment of the resultant force about any point. In this case, we can take moments about the current center of gravity (CG) of the 5.00 kg object to determine the location of the center of gravity of the additional 1.50 kg mass.
The moment of a force about a point is given by the product of the magnitude of the force and the perpendicular distance from the point to the line of action of the force. Since the gravitational force acting on the masses is the only force acting on the system, we can take moments of the weight of each mass about the CG of the 5.00 kg object.
The moment of the weight of the 5.00 kg object about its CG is zero, since the CG is the point about which the object is in rotational equilibrium. Therefore, we only need to consider the moment of the weight of the 1.50 kg mass about the CG of the 5.00 kg object.
The distance between the CG of the 5.00 kg object and the desired new CG is 1.60 cm to the left, so we need to find the distance between the current CG and the new CG. Let x be the distance from the current CG to the new CG.
The moment of the weight of the 1.50 kg mass about the current CG is:
(1.50 kg)(9.81 m/s²)(x) = 14.72x Nm
The moment of the weight of the 1.50 kg mass about the new CG is:
(1.50 kg)(9.81 m/s²)(1.60 cm + x) = 14.72x + 23.54 Ncm
Setting these two moments equal, we have:
14.72x Nm = 14.72x + 23.54 Ncm
Converting the units, we get:
0.1472x m = 0.2354 m
x = 1.60 cm (to two significant figures)
Therefore, the center of gravity of the additional 1.50 kg mass should be located 1.60 cm to the right of the current CG of the 5.00 kg object.
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Why is it called “static” electricity?
A. Charges can easily flow
B. Charges are not trapped in place
C. Charges cannot easily flow
D. Charges are free to move around
It is called static electricity because Charges cannot easily flow, hence option C is the answer.
Static electricity is called "static" because the charges are not free to move around easily. They tend to build up on the surface of an insulator and remain in place, rather than flowing like current in a conductor.
This buildup of charge can occur due to friction, induction, or any other mechanisms in the conductor. Therefore, option C is the correct option that says "Charges cannot easily flow".
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An experiment is conducted in which a cart travels across a horizontal surface and collides with a wall. Data collected from the experiment are used to create the graph of the cart’s velocity as a function of time. All frictional forces are considered to be negligible. Which data from the graph should the student use to determine the direction of the net force exerted on the cart and the direction of the change in momentum of the cart from the time intervals of A to B ?
The detail that the student will use to determine the direction of the net force exerted on the cart is The velocity.
How to get the detail from the graphWhen examining the velocity-time graph of a cart during time intervals A to B, it is crucial that we analyze it to determine both the net force's direction and the change in momentum's direction.
By observing the slope of the velocity-time graph, one can conclude the acceleration of the vehicle; if positive, then the acceleration moves mostly in a forward direction, but when negative, the opposite holds true, indicating the acceleration's backward motion towards initial position.
To get the direction of the change in momentum, you would have to analyze the slope of the velocity vs. time graph at the various time intervals.
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Solve pls:
a) What are the maina dvantages of an epicyclicgearbox? b) Figure Q4 overleaf shows a diagram for an epicyclic gear train. Power is supplied to
wheel 3 and is delivered to a load attached to the epicyclic arm, body 2. Wheel 5 is fixed to the gear case, body 1.
i) Determine T4 if t3 = 30, t4 = 40 and t5 = 60.
a) The main advantages of an epicyclic gearbox are:
High gear ratios can be achieved in a small space, making it a compact design.It can provide a smooth and efficient transfer of power due to the multiple contact points between gears.It can be used for different applications, such as increasing torque or speed, reversing direction, and providing a neutral point.How to solve a gearbox?b) i) Using the formula for the gear ratio of an epicyclic gear train:
T4/T3 = (t2/t1) x (t5/t2) x (t4/t5)
T4/30 = (1/2) x (60/20) x (40/60)
T4 = 40 Nm
ii) From the law of gearing for an epicyclic gear train:
w21 = (t3/t2) x (t5/t4) x w31 - (t3/t2) x w2
Substituting the given values:
w21 = (30/20) x (60/40) x 200 - (30/20) x 100
w21 = 150 rad/s
iii) The fixing couple that must be applied to wheel 5 can be found from the power transmitted by the gear train:
P = w3 x T3 = w2 x T2 = w1 x T1
Substituting the given values:
9 kW = 200 rad/s x 30 Nm = w2 x T2 = w2 x 20 Nm
w2 = 450 rad/s
T2 = (9 kW) / (450 rad/s) = 20 Nm
The fixing couple that must be applied to wheel 5 is equal in magnitude and opposite in direction to T2, so it is -20 Nm.
iv) The tangential force at the pitch point between wheels 3 and 4 can be found from the formula:
Ft = (2 x Pd) / (m x z3)
where Pd is the diametral pitch, m is the module, and z3 is the number of teeth on wheel 3.
Substituting the given values:
Pd = 25.4 / 5 = 5.08 teeth/inch
z3 = t3 / m = 30 / 5 = 6 teeth
Ft = (2 x 5.08) / (5 x 6) = 0.846 N
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A hydraulic system has two pistons. Input force on one piston is 15.8 lb and the other piston can lift a weight of 93 lb. What is the mechanical advantage?
Answer:
The mechanical advantage of a hydraulic system is given by the ratio of the output force to the input force. In this case, the input force is 15.8 lb and the output force is 93 lb.
So, the mechanical advantage of the hydraulic system is:
MA = Output force / Input force
MA = 93 lb / 15.8 lb
MA = 5.89
Therefore, the mechanical advantage of the hydraulic system is 5.89. This means that the system can lift a weight that is almost 6 times greater than the input force applied to the other piston.
Determine the resultant x and y components, when one vector is equal to 26.5 and the other 44 with angles of 56 and 28 degrees
The resultant x and y components are 53.23 and 41.51, respectively.
What are the components?
To determine the resultant x and y components of the vectors, we can use the following equations:
Rx = ΣFx = F1x + F2x + ...
Ry = ΣFy = F1y + F2y + ...
where F1x, F2x, ... are the x components of the vectors, F1y, F2y, ... are the y components of the vectors, and ΣFx and ΣFy are the total x and y components of the resultant vector, R.
First, we need to find the x and y components of each vector:
Vector 1: magnitude = 26.5, angle = 56°
F1x = 26.5cos(56) = 14.28
F1y = 26.5sin(56) = 21.44
Vector 2: magnitude = 44, angle = 28°
F2x = 44cos(28) = 38.95
F2y = 44sin(28) = 20.07
Now we can add the x and y components of the vectors to find the total x and y components of the resultant vector:
ΣFx = F1x + F2x = 14.28 + 38.95 = 53.23
ΣFy = F1y + F2y = 21.44 + 20.07 = 41.51
Therefore, the resultant x and y components are 53.23 and 41.51, respectively.
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A weather balloon used by meteorologists is made of a flexible bag that allows the gas inside freely expand. If a weather balloon containing 25.0 m^3 of helium gas  is released from sea level, what is the volume of gas when the balloon reaches a height of 2100 m, where the pressure is 0.82×10^5 PA? Assume the temperature is unchanged. 
The volume of the helium gas in the weather balloon, when it reaches a height of 2100 m, is 30.85 m^3.
To solve this problem, we can use the ideal gas law, which states that the product of the pressure (P), volume (V), and temperature (T) of an ideal gas is proportional to the number of particles of the gas (n) and the universal gas constant (R). Since the temperature is assumed to be constant, we can write:
P1V1 = P2V2
where P1 and V1 are the initial pressure and volume of the helium gas, and P2 and V2 are the pressure and volume at a height of 2100 m.
At sea level, the pressure is approximately 1.01×10^5 Pa, so we have:
P1 = 1.01×10^5 Pa
V1 = 25.0 m^3
At a height of 2100 m, the pressure is 0.82×10^5 Pa, so we can solve for V2:
P1V1 = P2V2
V2 = (P1*V1)/P2
V2 = (1.01×10^5 Pa * 25.0 m^3) / (0.82×10^5 Pa)
V2 = 30.85 m^3
Therefore, the volume of the helium gas in the weather balloon when it reaches a height of 2100 m is approximately 30.85 m^3.
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