Question

A sled with mass 8.00kg moves in a straight line on a frictionless horizontal surface. At one point in it's path, it's speed is 4.00 m/s; after it has traveled 2.5m beyond this point, it's speed is 6.00m/s. Use the work-energy theorem to find the 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

We will use two definitions to solve this problem. The first will be given by the conservation of energy, whereby the change in kinetic energy must be equivalent to work. At the same time, work can be defined as the product between the force by the distance traveled. By matching these two expressions and clearing for the Force we can find the desired variable.

$W = KE_f-KE_i$

$Fd = \frac{1}{2}mv_f^2-\frac{1}{2} mv_i^2$

Thus the force acting on the sled is,

$F = \frac{m}{2s} (v_f^2-v_i^2)$

Replacing,

$F = \frac{8}{2(2.5)}(6^2-4^2)$

$F = 32N$

Therefore the Force acting on the sled is 32N