Question

When two people push in the same direction on an object of mass m, they cause an acceleration of magnitude a1. When the same people push on the object in opposite directions, the acceleration of the object has the magnitude a2.

Determine the magnitude of the force exerted by each of the two people in terms of m, a1,and a2.

Answer 1

Each person exerts a force of F1 = (m * a1) / 2 when pushing together in the same direction on an object, based on the relationship Fnet = ma. This also represents the individual force when they push in opposite directions, leading to no net acceleration.

Step-by-step explanation:

When two people push in the same direction on an object, and they cause an acceleration a1, the combined force F exerted is F = m * a1 because of Newton's second law Fnet = ma. When they push in opposite directions leading to acceleration a2, the net force is the difference between the two forces, since one force is acting against the other. Thus, the net force in this case is also m * a2.

Let F1 be the force exerted by each person. When pushing together, the net force is 2F1 = m * a1. When pushing against each other, the net force is F1 - F1 = m * a2 (which is essentially zero since the forces cancel each other out).

From the first scenario, solving for F1 gives us F1 = (m * a1) / 2. This is the force exerted by each of the two people when they push together in the same direction, and coincidentally, it is also the force exerted when they push in opposite directions as evidenced by the zero resultant force when a2 is the acceleration experienced.