An Unfair Race This applet shows the results of releasing a frictionless block and a rolling disk with equal masses from the top of identical inclined planes.
Which of the following is the best explanation of the results shown in the applet?
A) The disk loses energy to friction as it rolls, but the box is frictionless and so it speeds up more quickly and gets to the bottom first.
B) The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy.
C) The net forces on the two objects are equal, but the force on the disk gets partially used up in creating the torque necessary to make it roll.
D) The net forces on the two objects are equal, but the force on the disk is not directed parallel to the ramp, and so does not create as great an acceleration down the ramp.

B) The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy.

I had the same question before and B is the most logical answer and it is correct.

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moya1316 moya1316 · Answer 2 · 2021-11-26T13:31:52+01:00

The law of conservation of energy allows finding the result for the answers that best explains the the difference in the descent of the bodies down the ramp is:

B) The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy.

The conservation of energy is one of the most important principles of physics, it establishes that energy cannot be created or destroyed only by transforming it.

Mechanical energy is the sum of kinetic energy and potential energy.

Let's look for the mechanical energy of each body, let's start with the box.

Starting point highest part of the ramp.

Em₀ = U = m g h

final point. Lower part of the ramp.

Em_f = ½ m v²

Indicate that there is no friction, the energy is conserved.

m g h = ½ m v²

v² =2gh

We write the energy for the disk, we must take into account that the disk in addition to having a linear movement is rotating movement.

Starting point. Highest part.

Em₀ = U = m g h

Final point. Low point

Emf = [tex]K_{liear} + K_{rotation}[/tex]

Emf = ½ mv² + ½ I w²

The linear and rotational variables are related

v = w r

w = v / r

we substitute

Emf = ½ m v² + ½ I [tex]\frac{v^2}{r^2}[/tex]

energy is conserved

Em₀ = Em_f

m g h = ½ m v² ( [tex]1 + \frac{I}{mr^2}[/tex] )

v² = [tex]\frac{2gh}{1+ \frac{I}{mr^2} }[/tex]

which we see the linear velocities of the box and the disk the disk has lower speed, this is because part of the energy is spent in creating the rotational movement.

Let's analyze the answers:

A) False. The point of contact of the disc with the surface does not move, therefore it does not lose energy by friction.

B) True. According to the analysis above, for the energy is transformed into linear speed and part into rotational speed.

C) False. The force are the same, but the torque that makes the disc roll comes from the frictional force at the point of contact between the disc and the ramp, not from weight.

D) False. The two forces are vertical because it is the weight of the body.

In conclusion, using the law of conservation of energy we can find the result for the answers that best explains the descent down the ramp is:

B) The potential energy of the disk is converted into translational and rotational kinetic energy, so the translational speed grows more slowly than that of the box, which has no rotational energy.

Learn more here: brainly.com/question/11695177