A block and a spool have the same mass, and are each pulled across a level, frictionless surface by a string, as shown to the right. The string pulling the spool is wrapped around it many times, and the other string is fastened to the center of the block. Both hands pull with the same force, starting at the same instant, and maintain a constant tension.

A) Describe how each object moves on the frictionless surface in terms of both translation and rotation.

B) Does the hand pulling the spool’s string move faster, slower, or at the same speed as the other hand in order to maintain the same tension in the strings? Explain.

C) Which object, if either, passes the finish line first? Explain your reasoning.

frictionless? think on the spool, would it rotate? it has a force on it (either above the cg or below, I dont have a picture), but would it rotate? I suspect your teacher wants you to consider a mimimal friction...

A) Both the block and the spool will undergo both translation and rotation on the frictionless surface.

The block will experience pure translation, meaning it will move in a straight line without any rotation. The force applied through the center of the block will result in an equal and opposite force pushing the block forward, causing it to move without any rotation.

On the other hand, the spool will experience both translation and rotation. The force applied through the string wrapped around the spool will cause it to rotate in addition to moving in a straight line. As the string is pulled, it unwinds from the spool, causing it to rotate. The rotation is a result of the torque applied by the tension in the string.

B) The hand pulling the spool's string will move slower than the other hand in order to maintain the same tension in the strings.

The tension in a string is transmitted unchanged throughout its length. In this scenario, the same tension is applied to both strings. Since the spool has a greater distance over which the tension is applied due to the wrapping of the string, the spool experiences a larger torque, resulting in a larger rotational force. To balance out this increased rotational force, the speed of the hand pulling the spool's string needs to be slower.

C) The block and the spool will cross the finish line at the same time.

Since both the block and the spool have the same mass and experience the same force and tension, the only difference is the rotation experienced by the spool. However, the rotation does not affect the speed at which it moves in translation. Therefore, both objects will move at the same speed, and hence, they will cross the finish line at the same time.

A) The block will only experience translation since the string is directly fastened to its center. It will move in a straight line along the surface.

The spool, on the other hand, will have both translational and rotational motion. The string wrapped around the spool will cause it to rotate as it is pulled. At the same time, the spool will also have translational motion in the same direction as the block's movement.

B) The hand pulling the spool's string will move faster than the other hand to maintain the same tension in the strings. This is because the spool has rotational motion in addition to translational motion. The rotational motion causes the string to unwind from the spool, resulting in a larger distance traveled by the hand compared to the block.

C) The spool will pass the finish line first. This is because the spool has both translational and rotational motion, allowing it to cover a larger distance than the block. Even though the hands are exerting the same force and maintaining the same tension in the strings, the spool's rotational motion allows it to move faster.