A box weighing 65.0 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.
Part a) Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs 24.0 N .
Part b) Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs 43.0 N .
part c)Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs 82.0 N .
m•g = 65 N, m1•g =24 N, m2•g =23 N, m3•g =82 N
Tthe force that the table exerts on the box is the normal reaction
(a) N =m•g –T1 = m•g –m1•g =
= 65 – 24 = 41 N,
(b) N =m•g –T2 = m•g –m2•g =
= 65 – 43 = 22 N,
(c) N =0.
The box is moving at the acceleration
a = g•(m3-m)/(m3+m)
Part a) Well, the table is clearly shouldering all the weight of the world... well, I mean, the box. So the force that the table exerts on the box will be equal to the weight of the box, which is 65.0 N.
Part b) Ah, the weight got a bit heavier, huh? No worries, the table is up for the challenge! The force that the table exerts on the box will still be equal to the weight of the box, which is 65.0 N.
Part c) Oh boy, that weight is really testing the limits of our poor table now. The force that the table exerts on the box will still be equal to the weight of the box, which is 65.0 N. But maybe it's time for the table to hit the gym and build some muscles! 🏋️♀️
In order to solve this problem, we need to understand the forces acting on the box and the pulley.
Let's define the following forces:
- F_box: the force exerted by the table on the box
- F_tension: the tension in the rope
- F_weight: the weight of the hanging object
Given:
- F_weight = 24.0 N, 43.0 N, and 82.0 N for parts a, b, and c respectively
- F_box = 65.0 N
We need to consider two cases:
Case 1: F_weight < F_box
In this case, the box is heavier than the hanging object. The tension in the rope is given by F_weight, and the force exerted by the table on the box is equal to the weight of the box.
Part a) F_box = 65.0 N
Part b) F_box = 65.0 N
Part c) F_box = 65.0 N
Therefore, the force that the table exerts on the box is 65.0 N for all three cases.
Case 2: F_weight > F_box
In this case, the hanging object is heavier than the box. The tension in the rope is equal to F_box (the weight of the object), and the force exerted by the table on the box is the difference between the weight of the box and the tension in the rope.
Part a) F_tension = 24.0 N
F_box = 65.0 N
F_table = F_box - F_tension = 65.0 N - 24.0 N = 41.0 N
Part b) F_tension = 43.0 N
F_box = 65.0 N
F_table = F_box - F_tension = 65.0 N - 43.0 N = 22.0 N
Part c) F_tension = 65.0 N (maximum tension the rope can handle)
F_box = 65.0 N
F_table = F_box - F_tension = 65.0 N - 65.0 N = 0 N
Therefore, the force that the table exerts on the box is 41.0 N for part a), 22.0 N for part b), and 0 N for part c).
To determine the force that the table exerts on the box in each scenario, we need to consider the forces acting on the box. The box is in equilibrium, which means that the net force acting on it is zero.
In this case, there are two forces acting on the box: the weight of the box itself and the tension in the rope due to the weight hanging on the other side of the pulley.
Let's calculate the force that the table exerts on the box in each scenario:
Part a) The weight hanging on the other side of the pulley weighs 24.0 N.
Since the box is in equilibrium, the force that the table exerts on the box must be equal in magnitude but opposite in direction to the combined weight of the box and the weight hanging on the other side of the pulley. Therefore, the force that the table exerts on the box is the sum of these two weights:
Force on the box = Weight of the box + Weight hanging on the other side of the pulley
= 65.0 N + 24.0 N
= 89.0 N
Part b) The weight hanging on the other side of the pulley weighs 43.0 N.
Using the same reasoning as above, the force that the table exerts on the box is:
Force on the box = Weight of the box + Weight hanging on the other side of the pulley
= 65.0 N + 43.0 N
= 108.0 N
Part c) The weight hanging on the other side of the pulley weighs 82.0 N.
Again, applying the same logic, the force that the table exerts on the box is:
Force on the box = Weight of the box + Weight hanging on the other side of the pulley
= 65.0 N + 82.0 N
= 147.0 N
Therefore, the force that the table exerts on the box varies depending on the weight hanging on the other side of the pulley: 89.0 N for Part a), 108.0 N for Part b), and 147.0 N for Part c).