Question

a sled with mass 12kg moves in a straight line on a frictionless, horizontal surface at one point in its path, its speed is 4m/s; after it has traveled 2.50m beyond this point, its speed is 6m/s use the work-energy theorem to find the net force acting on the sled, assuming that this force is constant and that it acts in the direction of the sled's motion

Answer 1

The net force acting on the sled is 48 N in the direction of the sled's motion.

Step-by-step explanation:

The student's question involves a sled of mass 12 kg moving on a horizontal, frictionless surface and experiencing a constant net force that changes its speed from 4 m/s to 6 m/s over a distance of 2.50 m. To find the net force acting on the sled, we can use the work-energy theorem, which states that the work done on the sled is equal to the change in its kinetic energy.

First, we find the initial and final kinetic energies:

• Initial kinetic energy, Ki = 0.5 x m x vi2 = 0.5 x 12 kg x (4 m/s)2 = 96 J
• Final kinetic energy, Kf = 0.5 x m x vf2 = 0.5 x 12 kg x (6 m/s)2 = 216 J

Then, we calculate the work done (W) as the difference in kinetic energy:

W = Kf - Ki = 216 J - 96 J = 120 J

Since work is also the product of force (F) and distance (d) when force is constant and acts in the direction of motion, we have:

W = F x d

Therefore, the net force (F) can be determined as follows:

F = W / d = 120 J / 2.50 m = 48 N

The net force acting on the sled is 48 N in the direction of the sled's motion.