Question

A 86-kg parent and a 23-kg child meet at the center of an ice rink. They place their hands together and push.

If the acceleration of the child is 0.31 m/s² in magnitude, what is the magnitude of the parent's acceleration?

Answer 1

The magnitude of the parent's acceleration is 0.083 m/s².

Step-by-step explanation:

To find the magnitude of the parent's acceleration, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. If the child has an acceleration of 0.31 m/s², we can calculate the force exerted on the child using the equation F = ma, where F is the force, m is the mass, and a is the acceleration. So, the force exerted on the child is:

Fchild = (23 kg)(0.31 m/s²) = 7.13 N

Since the parent and child are pushing against each other, the force exerted on the parent is equal in magnitude but opposite in direction to the force exerted on the child. Therefore, the force exerted on the parent is also 7.13 N. To find the parent's acceleration, we rearrange the equation F = ma to solve for acceleration:

a = F/m

Using the values F = 7.13 N and m = 86 kg, we can calculate the parent's acceleration as:

a = (7.13 N)/(86 kg) = 0.083 m/s²

So, the magnitude of the parent's acceleration is 0.083 m/s².