Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B.Both carts start from rest.The velocities $\overrightarrow { \mathbf { v } }$ _A and $\overrightarrow { \mathbf { v } }$ _B of the bodies at the end of distance D are related by A) $\overrightarrow { \mathbf { v } }$ _B = $\overrightarrow { \mathbf { v } }$ _A . B) $$\overrightarrow { \mathbf { v } }$$ _B = $$\sqrt { 2 }$$ $\overrightarrow { \mathbf { v } }$ _A. C) $\overrightarrow { \mathbf { v } }$ _B = 2 $\overrightarrow { \mathbf { v } }$ _A. D) $\overrightarrow { \mathbf { v } }$ _B = 4 $\overrightarrow { \mathbf { v } }$ _A. E) $\overrightarrow { \mathbf { v } }$ _A = 2 $\overrightarrow { \mathbf { v } }$ _B.

Question

Quizplus · Accepted Answer

The work done on each cart is equal to the force times the distance. Since the force on B is twice that on A, the work done on B is twice that on A. The work-energy principle states that the work done is equal to the change in kinetic energy. Therefore, the kinetic energy of B is twice that of A. Since kinetic energy is proportional to the square of velocity, $\overrightarrow { \mathbf { v } }$ _B = $\sqrt { 2 }$ $\overrightarrow { \mathbf { v } }$ _A.

Carts a and B Have Equal Masses and Travel Equal v→\overrightarrow { \mathbf { v } }v

Carts a and B Have Equal Masses and Travel Equal $\overrightarrow { \mathbf { v } }$