Physics

Problem

0.16\,\text{kg}

hockey puck slides on frictionless ice with an initial speed of

12\,\text{m}\,\text{s}^{-1}

toward a stationary robotic stick. Beginning at

t=0

, the stick exerts a horizontal force on the puck that varies with time as follows: • From

t = 0

t = 0.050\,\text{s}

, the force increases linearly from

0

F_{\max}

. • From

t = 0.050\,\text{s}

t = 0.20\,\text{s}

, the force decreases linearly back to

0

. After

t = 0.20\,\text{s}

the puck experiences no horizontal force. The stick is adjusted so that the puck comes precisely to rest at

t = 0.20\,\text{s}

(immediately after the force returns to zero). a. Part 1: (a) Derive an algebraic expression for

F_{\max}

in terms of the puck’s mass

m

, its initial speed

v_0

, and the times

t_1 = 0.050\,\text{s}

and

t_2 = 0.20\,\text{s}

. Clearly state each step in your reasoning. b. Part 2: (b) Using the given numerical values, calculate

F_{\max}

. c. Part 3: (c) Determine the average power delivered to the puck during the interval

0 \le t \le t_1