Question

a freight company uses a compressed spring to shoot 2.0kg packages up a 1.0m high frictionless ramp into a truck. The spring constant is 500N/m and the spring is compressed 30cm

Answer 1

let speed of the package when it reaches top is v.

as there is no friction, work done against friction=0

and total mechanical energy is conserved.

hence initial potential energy of the spring=final potential energy of the package+final kinetic energy of the package

==>0.5*spring constant*compression^2=mass*g*height+0.5*mass*speed^2

==>0.5*500*0.3^2=2*9.8*1+0.5*2*v^2

==>22.5=19.6+v^2

==>v=sqrt(22.5-19.6)=1.70293 m/s

hence speed of the package when it reaches the top of the ramp is 1.70293 m/s