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
[tex]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}[/tex]
#Denote the stopping distance and force required with a prime and observe from (i) that:
[tex]F\infty\frac{1}{\bigtriangleup x}\\\\F\prime =F.\frac{\bigtriangleup x}{(\bigtriangleup x)\prime}\\\\[/tex] #If stopping distance increases by a factor of 79/50;
[tex]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}[/tex]
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.
