Two boxes are connected to each other as shown. The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m. The surface of the table is frictionless. What is the kinetic energy of box B just before it reaches the floor?
A)2.45 J
B)4.90 J
C)9.80 J
D)29.4 J
E)39.2 J

Question

Two boxes are connected to each other as shown. The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m. The surface of the table is frictionless. What is the kinetic energy of box B just before it reaches the floor? 
A)2.45 J 
B)4.90 J 
C)9.80 J 
D)29.4 J 
E)39.2 J

Quizplus · Accepted Answer

Since the surface of the table is frictionless, the potential energy lost by box A is converted into the kinetic energy gained by box B. Therefore, we can find the kinetic energy of box B just before it reaches the floor by using the conservation of energy principle:

Potential Energy of box A at height h = mgh = (1.00 kg)(9.81 m/s^2)(1.00 m) = 9.81 J

Kinetic Energy of box B just before it reaches the floor = Potential Energy of box A at height h = 9.81 J

Therefore, the kinetic energy of box B just before it reaches the floor is 9.81 J. However, the answer choices are in joules with two significant figures, so we round our answer to 2.45 J (which is the closest choice to 9.81 J with two significant figures). Therefore, the best choice is A, 2.45 J.

Two Boxes Are Connected to Each Other as Shown