A hockey puck slides in the direction on very smooth ice

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

0.45\,\text{kg}

hockey puck slides in the

+x

direction on very smooth ice. Beginning at

x=0

, a horizontal force

F_x

that is directed along

+x

acts on the puck over the interval

0\le x\le10\,\text{m}

. The magnitude of

F_x

varies with position as follows: • For

0\le x\le4.0\,\text{m}

F_x=3.0\,\text{N}

(constant). • For

4.0\,\text{m}<x\le7.0\,\text{m}

F_x

decreases linearly with

x

from

3.0\,\text{N}

x=4.0\,\text{m}

0.50\,\text{N}

x=7.0\,\text{m}

. • For

7.0\,\text{m}<x\le10\,\text{m}

F_x

is constant at

0.50\,\text{N}

. At

x=0

the puck’s speed is

1.5\,\text{m/s}

. Friction and air resistance are negligible. (a) Calculate the total work done on the puck by the force

F_x

as it travels from

x=0

x=10\,\text{m}

. Show all steps, including any geometric interpretations you use. (b) Determine the speed of the puck at

x=10\,\text{m}

. (c) On the axes below, sketch a qualitative graph of the puck’s kinetic energy

K

versus position

x

for the interval

0\le x\le10\,\text{m}

. Label key values of

x

that correspond to changes in the slope of your graph. (Numerical scales are not required.)