AP Physics 1 Question 349: Answer and Explanation
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7. Two objects, a sphere and a block of the same mass, are released from rest at the top of an inclined plane. The sphere rolls down the inclined plane without slipping. The block slides down the plane without friction. Which object reaches the bottom of the ramp first?
- A. The sphere, because it gains rotational kinetic energy, but the block does not
- B. The sphere, because it gains mechanical energy due to the torque exerted on it, but the block does not
- C. The block, because it does not lose mechanical energy due to friction, but the sphere does
- D. The block, because it does not gain rotational kinetic energy, but the sphere does
Correct Answer: D
Both objects begin with no kinetic energy, and they undergo the same decrease in potential energy. Therefore, they finish with the same total kinetic energy. The block doesn't have any rotational K, so all of its K is translational. But the sphere is rotating, so some of its K is translational, and some is rotational:
Ktotal, block = Ktotal, sphere Ktrans, block + 0 = Ktrans, sphere + Krot, sphere
Thus, once they start moving, the block has more Ktrans than the sphere. Its center moves faster, so the block finishes first.