The drawing shows box 1 resting on a table, with box 2 resting on top of box 1. A massless rope passes over a massless, frictionless pulley. One end of the rope is connected to box 2 and the other end is connected to box 3. The weights of the three boxes are W1 = 51.4 N, W2 = 33.5 N, and W3 = 25.5 N. Determine the magnitude of the normal force that the table exerts on box 1
To determine the magnitude of the normal force that the table exerts on box 1, we need to analyze the forces acting on box 1.
First, let's consider the weight of box 1. The weight is a downward force equal to W1 = 51.4 N.
Next, let's look at the tension in the rope connected to box 1. Since the rope is massless, the tension is the same on both sides of the pulley. This means the tension in the rope connected to box 1 is equal to the tension in the rope connected to box 2. Let's call this tension T.
Now, the tension T is essentially supporting the weight of box 2, which is downward with a force of W2 = 33.5 N. Therefore, the tension T must be equal to W2.
Finally, the normal force is the force exerted by a surface perpendicular to the surface. In this case, the table exerts a normal force upward on box 1.
To find the magnitude of the normal force, we need to balance the forces on box 1. The downward forces are the weight of box 1 (W1) and the tension in the rope connected to box 1 (T = W2). The upward force is the normal force.
Therefore, we can write the equation: Normal force + T - W1 = 0
Substituting the values, we have: Normal force + 33.5 N - 51.4 N = 0
Solving for the normal force, we get: Normal force = 51.4 N - 33.5 N
Calculating the value gives us: Normal force = 17.9 N
So, the magnitude of the normal force that the table exerts on box 1 is 17.9 N.