A 12.5-kg crate slides along a horizontal frictionless surface at a constant speed of 4.0 m/s. The crate then slides down a frictionless incline and across a second horizontal surface as shown in the figure.
-What is the speed of the crate when it arrives at the lower surface?
A)7.7 m/s
B)8.6 m/s
C)59 m/s
D)75 m/s
E)98 m/s

Question

A 12.5-kg crate slides along a horizontal frictionless surface at a constant speed of 4.0 m/s. The crate then slides down a frictionless incline and across a second horizontal surface as shown in the figure. 
-What is the speed of the crate when it arrives at the lower surface?
A)7.7 m/s 
B)8.6 m/s 
C)59 m/s 
D)75 m/s 
E)98 m/s

Quizplus · Accepted Answer

Since there is no friction, the total mechanical energy of the system (crate + Earth) is conserved.

At the top of the incline, the crate has only gravitational potential energy because it is not moving.

PE = mgh = (12.5 kg)(9.8 m/s^2)(2.0 m) = 245 J

When the crate reaches the bottom of the incline, all of the potential energy has been converted to kinetic energy.

KE = 1/2mv^2

245 J = 1/2(12.5 kg)v^2

v^2 = (2 * 245 J) / 12.5 kg = 38.4 m^2/s^2

v = sqrt(38.4 m^2/s^2) = 6.20 m/s

Since there is no friction on the second horizontal surface, the crate maintains this speed as it moves along it.

Adding the speed from the first surface (4.0 m/s) gives the final speed:

Final speed = 6.20 m/s + 4.0 m/s = 10.2 m/s

Therefore, the answer is B) 8.6 m/s, which is the closest choice to 10.2 m/s.

A 125-Kg Crate Slides Along a Horizontal Frictionless Surface at a a Constant