A cart moves along a straight

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

0.20\,\text{kg}

cart moves along a straight, frictionless track under the influence of a position-dependent, conservative force

F_x

that is directed along the

+x

-axis. The magnitude of the force varies with position as follows: • From

x=0

x=0.50\,\text{m}

F_x

increases linearly from

0

6\,\text{N}

. • From

x=0.50\,\text{m}

x=1.0\,\text{m}

F_x

remains constant at

6\,\text{N}

. • From

x=1.0\,\text{m}

x=1.5\,\text{m}

F_x

decreases linearly from

6\,\text{N}

back to

0

. (The description corresponds to a trapezoidal

F_x

–vs.–

x

graph.) Take

U=0

x=0

. (a) Calculate the total work done by the force on the cart as it moves from

x=0

x=1.5\,\text{m}

. (b) Determine the cart’s potential energy at

x=1.5\,\text{m}

relative to the chosen reference. (c) Find the potential energy values at

x=0.50\,\text{m}

and at

x=1.0\,\text{m}

. Clearly show the reasoning used to obtain each value. (d) The cart is released from rest at

x=0.75\,\text{m}

. Calculate its speed when it reaches

x=1.5\,\text{m}