A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure.
-What is the final speed of the crate?

Question

A 325-N force accelerates a 50.0-kg crate from rest along a horizontal frictionless surface for a distance of 20.0 m as shown in the figure. 
-What is the final speed of the crate?

Quizplus · Accepted Answer

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. That is, W = delta(K), where W is the work done, delta(K) is the change in kinetic energy.

Here, the initial kinetic energy of the crate is zero since it starts from rest. Thus, the work done by the 325-N force is equal to the final kinetic energy of the crate.

The work done by the force over a distance of 20 meters is:

W = F*d*cos(theta) = 325 N * 20 m * cos(0) = 6500 J

Since the crate has mass of 50 kg, its final kinetic energy is:

K = (1/2)*m*v^2 = (1/2)*50 kg * v^2

Setting the work done by the force equal to the final kinetic energy:

6500 J = (1/2)*50 kg * v^2

v^2 = 260 m^2/s^2

Taking the square root of both sides gives:

v = 16.1 m/s

Therefore, the final speed of the crate is 16.1 m/s, or choice (B)

A 325-N Force Accelerates a 50