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A block with mass 12.0 kg is being pushed along a horizontal floor by a force P as shown in the following diagram. At clock reading *t*=0.00 s and position *x* =
0.00 m the block has an instantaneous velocity of 2.00 m/s. The angle
is θ = 0.35 rad. The force P is applied to the block at the instant
it is in position *x* = 0.00 m. The direction of P remains fixed, but its magnitude varies with position as shown in the graph at the right. The coefficient of sliding friction between the block and the floor is 0.2.

- Calculate the velocity the box has at the position
*x*= 4.00 m by calculating the net work done on the block during the diplacement and finding the final kinetic energy. - Try doing the calculation of the final velocity using Newton's second law and the definitions of velocity and acceleration. If you get stuck, explain you difficulty in completing the calculation.
- Calculate and describe any internal
*thermal*energy changes of the block-floor system over the entire history of the motion dealt with above. - Calculate the momentum of the block at position
*x*= 4.00 m, the momentum*change*imparted to the block over the interval between positions*x*= 0.00 and*x*= 4.00 m, and the net impulse that must have been delivered to the block over this interval.

* Based on a problem in [Arons 1990].

Page last modified November 7, 2004: PE22