A spring,with k = 2500 N/m,is fixed vertically to the floor.A 10.0-kg box is pressed down on the spring such that the total compression of the spring is 0.5 m.When the box is released,what is the maximum speed the box reaches?

Question

Quizplus · Accepted Answer

The potential energy stored in the spring is given by:
PE = (1/2)kx^2
where k is the spring constant and x is the compression of the spring.

In this case, the maximum compression of the spring is 0.5 m, so the potential energy stored in the spring when the box is pressed down is:
PE = (1/2)(2500 N/m)(0.5 m)^2 = 625 J

When the box is released, this potential energy is converted to kinetic energy, so we have:
KE = (1/2)mv^2
where m is the mass of the box and v is its velocity.

Solving for v, we get:
v = sqrt((2KE)/m)

Substituting the values we know, we get:
v = sqrt((2(625 J))/(10.0 kg)) = 7.25 m/s

Therefore, the answer is (B) 7.25 m/s.

A Spring,with K = 2500 N/m,is Fixed Vertically to the Floor.A