Your friend has a pie on the roof of his van. You are standing on the ground and observe the van stopping abruptly for a red light. The pie does not slip off the roof (a) Construct a motion diagram and a force diagram for the pie as the van approaches the red light, from your frame of reference and from the driver's frame of reference. (b) Repeat part (a) for the case when the light turns green. Be sure to specify the observer and identify the other object causing each force. (c) Are the motion diagrams consistent with the force diagrams for each case?
(a) From your frame of reference:
- Motion diagram: The pie appears to be at rest on the roof of the van.
- Force diagram: There are two forces acting on the pie - gravity (downward) and the normal force from the roof of the van (upward).
From the driver's frame of reference:
- Motion diagram: The pie appears to be moving forward with the van.
- Force diagram: There are two forces acting on the pie - the force from the van pushing it forward (in the direction of motion) and the normal force from the roof of the van (upward).
(b) From your frame of reference:
- Motion diagram: The pie remains at rest on the roof of the van.
- Force diagram: Same as in part (a).
From the driver's frame of reference:
- Motion diagram: The pie appears to move slightly backward and then settle back to its original position on the roof of the van.
- Force diagram: There are two forces acting on the pie - the force from the van pushing it forward (in the direction of motion) and the normal force from the roof of the van (upward).
(c) Yes, the motion diagrams are consistent with the force diagrams for each case in both frames of reference. In both cases, the normal force balances the force due to gravity to keep the pie in place on the roof of the van. The additional force in the driver's frame due to the van's acceleration in the forward and backward directions causes the slight movement of the pie observed in that frame.
(a) Motion Diagram: From your frame of reference, since the pie does not slip off the roof, the motion of the pie will be in the same direction and at the same speed as the van. Therefore, the motion diagram would show the pie moving forward in a straight line.
Force Diagram: From your frame of reference, the only force acting on the pie is the force of gravity acting vertically downward.
From the driver's frame of reference, the motion diagram would show the pie as stationary, as it is attached to the roof of the van.
The force diagram from the driver's frame of reference would also show the force of gravity acting vertically downward as the only force.
(b) Motion Diagram: From your frame of reference, when the light turns green and the van starts to move, the motion diagram would show the pie moving forward together with the van.
From the driver's frame of reference, the motion diagram would show the pie remaining stationary as it is still attached to the roof of the van.
Force Diagram: From your frame of reference, the only force acting on the pie would still be the force of gravity acting vertically downward.
From the driver's frame of reference, the only force acting on the pie would still be the force of gravity acting vertically downward.
(c) The motion diagrams from both frames of reference are consistent with the force diagrams for each case. In both cases, the only force acting on the pie is the force of gravity, regardless of the frame of reference. This is why the pie does not slip off the roof.