The only force acting on a 2.0-kg body as it moves along the x axis is given by F_x = (12 − 2.0x) N, where x is in m. The velocity of the body at x = 2.0 m is 5.5 m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction? A) 36 J B) 39 J C) 43 J D) 46 J E) 30 J

Question

Quizplus · Accepted Answer

To find the maximum kinetic energy, we need to find the point where the net force on the body becomes zero, which is where the kinetic energy will be at a maximum.

FS1U1B1xS1U1B0 = (12 − 2.0x) N is the only force acting on the body in the +x direction.

Setting this force equal to zero, we get:

12 − 2.0x = 0

x = 6 m

This means that the maximum kinetic energy is attained at x = 6 m.

To find the kinetic energy at x = 2.0 m, we can use the work-energy principle:

W = ∆K

Where W is the work done by the net force on the body, and ∆K is the change in kinetic energy of the body.

W = ∫FS1U1B1xdx from x=0 to x=2 = ∫(12 − 2.0x)dx from x=0 to x=2 = (24 J)

At x = 2.0 m, the kinetic energy is:

K = 1/2mv² = 1/2(2.0 kg)(5.5 m/s)² = 30 J

The maximum kinetic energy is attained at x = 6 m, so we need to find the work done by the net force between x = 2.0 m and x = 6 m:

W = ∫FS1U1B1xdx from x=2 to x=6 = ∫(12 − 2.0x)dx from x=2 to x=6 = (48 J)

The maximum kinetic energy is:

Kmax = K + W = 30 J + 48 J = 78 J

However, we need to be careful, as the question asks for the maximum kinetic energy attained while moving in the +x direction. At x = 6 m, the body changes direction and starts moving in the -x direction. So, the maximum kinetic energy attained while moving in the +x direction is:

Kmax(+x) = 1/2mv² = 1/2(2.0 kg)(5.5 m/s)² = 30 J

Therefore, the best choice is D, 46 J.

The Only Force Acting on a 2