120 Bumper cart A 200 kg bumper cart can move on a rough horizontal surface. The

Question

120 Bumper cart A 200 kg bumper cart can move on a rough horizontal surface. The cart is pushed agains spring, with spring constant 6000 N/m, compressing it by 0.25 m. It is released and begins t move right. The coefficient of friction between the cart and the surface is 0.20. a) Determine the speed of the cart at the moment that it leaves the spring. b) Suppose that while the cart moves right it is also pulled with a rope that pulls with tension 400N to the right. Determine the speed of the cart when it leaves the spring.

Explanation / Answer

part a:

let speed at the moment it leaves the spring is v m/s.

using work energy principle:

potential energy in the spring - work done against friction=kinetic energy of the cart

==>0.5*spring constant*compression^2-friction force*distance travelled=0.5*mass*speed^2

==>0.5*6000*0.25^2-(0.2*200*9.8)*0.25=0.5*200*v^2

==>v=0.946 m/s

part b:

in the work energy principle, work done by the rope is to be added.

modified equation would be:

potential energy in the spring - work done against friction+work done by the rope=kinetic energy of the cart

==>0.5*spring constant*compression^2-friction force*distance travelled+tension in rope*distance travelled=0.5*mass*speed^2

==>0.5*6000*0.25^2-(0.2*200*9.8)*0.25+400*0.25=0.5*200*v^2

==>v=1.3766 m/s

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