A box weighing 77.0 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end (Fig. 4–45). Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Here's a free body diagram of the box that's on the table, there's a force exerted upwards and due to the hanging weight on the other side of the pulley, and this force up is due to the weight will be equal to the weight of the weight. And there's also going to be a normal force upwards on this box due to the table. And the box has a gravity force downwards of 77.0 Newtons. So, the net force on this box is zero because it's not accelerating and that means the up forces equal the down forces. So, the up force total is the normal force plus the force of the weight that's hanging, and that equals the down force total which is just gravity. And we can solve for the normal force by subtracting force of the weight from both sides. So, the normal force is Fg minus Fw. So, in part A that's 77 Newtons minus the 30 Newtons of the hanging weight which is 47 Newtons upwards. And then in Part B it's 77 minus 16 Newtons, so, that's that 17 Newtons normal force. And then in Part C there's no normal force since the hanging weight has a weight of 90 Newtons which is greater than the weight of this box and so the box won't even be touching the floor and so the floor will not be exerting any normal force at all because this box is going to accelerate upwards.