Net force of a drinking glass

Question

In order to drink from your glass you first need to lift it to your mouth. As you begin to lift your 0.20kg glass of water it is accelerating upwards at 0.090 m s^-2.

a) what is the net force acting on the glass?

b) What force are you applying to the glass?

c) What force is the glass applying to you?

Answer 1

a) This part is pretty straightforward. Newton's Second Law of Motion tells us that the acceleration of an object equals the net force acting on the object divided by its mass. We sometimes rearrange the order and write it

F_net = ma.

Since they told us the mass and acceleration of the glass, we know the net force. Also, keep in mind that the net force has a direction and that it is the same direction as the acceleration (in this case, up).

b) Here we have to assume that the glass is being lifted straight up and that no other forces are acting on the glass besides our hand and the gravitational force of the Earth. With that being the case, we draw a force diagram of the glass and find that we have the force of our hand directed up and the force of gravity directed down. The net force, therefore, is the vector sum of these two forces (assuming up is positive)

F_net = F_hand - F_g.

F_g = mg, so F_g = (0.2kg)(9.8m/s²) = 1.96N. Substitute our answer to part (a) for F_net and solve for F_hand. (Be sure to include the direction of the force of the hand on the glass when you give your final answer.)

c) Newton's Third Law of Motion tells us that when object A exerts a force on object B, that object B exerts an equal and opposite force on object A. So, the force of the glass on the hand is equal in magnitude and opposite in direction to the force of the hand on the glass (answer (b)).