# A person of weight 600N is pushing downward on a box, whose weight is 200N. If the contact force of the box on the ground is 300N, find the following.  a) The contact force of the person on the...

A person of weight 600N is pushing downward on a box, whose weight is 200N. If the contact force of the box on the ground is 300N, find the following.

a) The contact force of the person on the ground

b) The force of the box on the person’s hand

txmedteach | High School Teacher | (Level 3) Associate Educator

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The answer to this question lies in Newton's Third Law: for every action, there is an equal and opposite reaction. We know the person is pushing down on the box. Therefore, the box is pushing up on the person!

With how much force is the box pushing up on the person? Well, We know the box weighs 200 N. However, the downward force exerted by the box when the person is pressing on it is 300 N. Therefore, the person must be applying 100 N of force downward on the box. By Newton's Third Law, then, the box is applying 100 N of force upward on the person's hand! This answers the second part of the question.

To answer the first part, we simply draw a force diagram of the person. We know the person's weight is 600 N and it is a downward force. The only other force to act on the person is that which is applied by the box as a reaction to the downward force of 100 N that the person puts on it. Therefore, the only other force on the person is a 100 N upward force, giving us a net force of 500 N downward by the person before considering the contact force of the ground. Therefore, to be in equilibrium, the contact force must be 500 N upward to allow the net force to be zero.