Question

Suppose two children push horizontally, but in exactly opposite directions, on a third child in a sled. The first child exerts a force of 79 N, the second a force of 99 N, kinetic friction is 6.5 N, and the mass of the third child plus sled is 23 kg. AUsing a coordinate system where the second child is pushing in the positive direction, calculate the acceleration in m/s².

Answer 1

The acceleration of the sled is approximately 0.587 m/s² when the second child pushes in the positive direction with a force of 99 N, the first child pushes in the opposite direction with a force of 79 N, and the kinetic friction is 6.5 N and mass of the sled and child is 23 kg.

Step-by-step explanation:

Using a coordinate system where the second child is pushing in the positive direction, we will calculate the acceleration of the sled with the third child. Since the forces are applied horizontally and in opposite directions, we can consider the net force acting on the sled. To find the net force, we subtract the force exerted by the first child from the force exerted by the second child and then subtract the kinetic friction force Net force = Force by second child - Force by first child - Friction Net force = 99 N - 79 N - 6.5 N Net force = 13.5 N Now, we can calculate the acceleration using Newton's second law of motion, F = ma, where F is the net force, m is the mass, and a is the acceleration. According to Newton's second law: a = F/m a = 13.5 N / 23 kg a ≈ 0.587 m/s²