The block in the figure lies on a horizontal frictionless surface, and the sprin

Question

The block in the figure lies on a horizontal frictionless surface, and the spring constant is 46 N/m. Initially, the spring is at its relaxed length and the block is stationary at position X = 0. Then an applied force with a constant magnitude of 5.0 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. When that stopping, point is reached, what are (a) the position of the block, (b) the work that has been done on the block by the applied force, and (c) the work that has been done on the block by the spring force? During the block's displacement, what are (d) the block's position when its kinetic energy is maximum and (e) the value of that maximum kinetic energy?

Explanation / Answer

a)

The block will accelerate and then deccelerate since the force is of constant magnitude. Note that when the block

stops it is not in equilibrium.

using energy

F*x = 1/2*k*x^2

solve for x

x = F*2/k

x = 5*2/46

x = 0.22 m

b)

The work by the force is 5*x = 5*0.22 = 1.1 J


c)

This is equal to the energy stored in the spring = 1/2*46*0.22^2 = 1.1132 J

The work is -1.1132 J since it is now potential energy

d)

The block has max KE when the spring force is exaxtly equal to the spring force. Note that the block speeds up to

this point and slows down past this point

5 = k*x

x = 5/46 = 0.1087 m

e)

It is the work done by the force to that point minus the energy stored in the spring at that point

5*0.1087 - 1/2*46*0.1087^2 = 0.272 J

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