Question

A puck of mass m moving at speed v on a horizontal, frictionless surface is stopped in a distance d because a hockey stick exerts an opposing force of magnitude F on it. If the stopping distance d increases by 58 %, by what percent does the average force needed to stop the puck change, assuming that m and v are unchanged?

Answer 1

Answer:

-36.71%

Explanation:

Using the Generalized Work Energy Principle, the puck is brought to rest by an external force and the system has no kinetic energy

$U_i+W=U_f\\K_i+W=K_f\\\\0.5mv_i^2+F\bigtriangleup xcos\theta=0J\\\\0.5mv_i^2+F\bigtriangleup xcos180\textdegree=0J\\\\0.5mv_i^2=F\bigtriangleup x\\\\F=\frac{0.5mv_i^2}{2\bigtriangleup x}$

#Denote the stopping distance and force required with a prime and observe from (i) that:

$F\infty\frac{1}{\bigtriangleup x}\\\\F\prime =F.\frac{\bigtriangleup x}{(\bigtriangleup x)\prime}$  #If stopping distance increases by a factor of 79/50;

$F\prime=F.(79/50)^-^1\\\\F\prime=\frac{50F}{79}\\\\\therefore \bigtriangleup F=F\prime -F\\\\\bigtriangleup F=\frac{50F}{79}-F=-\frac{29F}{79}$

So F decreases by 36.71% . we expect force to reduce since the same amount of work is repeatedly done on the system over a long distance.