How Does a Pulley System Affect the Force Exerted by a Table on a Box?

[Natali]

Homework Statement

A box weighing 68 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.Determine the force that the table exerts on the box when weight hanging on the other side of the pulley is 27N.

Homework Equations

laws of motion

The Attempt at a Solution

draw free body diagram, fillin law, mg=27n
i have 2 divide mg by g to get m since the box does not move yet its accleration is 0 so mg = Fn? ?? except tension plays a role so how do i find Fn-Ft=mg?

 

[physics girl phd]

My first concern is that you really should draw two free body diagrams: One for the black hanging off the table, and one for the box resting on the table. The tension force connects these diagrams, because it's present on both objects.

In this case, you're right in that there is no acceleration, so the NET force on each object must be zero. This should help you solve for the values of unknown forces (tension in the rope and the normal/support force from the table on the box).

 

[baba89]

I would approach this problem by first drawing a free body diagram to visualize all the forces acting on the box. From the diagram, we can see that the weight of the box (68 N) is balanced by the normal force from the table. However, there is also a tension force in the rope due to the weight (27 N) hanging on the other end of the pulley.

To determine the force that the table exerts on the box, we can use Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. In this case, since the box is not moving, its acceleration is 0 and therefore the net force must also be 0. This means that the normal force from the table must be equal and opposite to the combined forces of gravity and tension in the rope.

We can set up an equation to represent this: Fn - (mg + T) = 0. Since we know the values of mg (68 N) and T (27 N), we can solve for Fn by rearranging the equation: Fn = mg + T = 68 N + 27 N = 95 N.

Therefore, the force that the table exerts on the box is 95 N. This shows that the table needs to exert a greater force than the weight of the box alone in order to balance out the additional weight hanging on the other end of the pulley.