Two strong magnets on opposite sides of a small table are shown. The long-range attractive force between the magnets keeps the lower magnet in place. Suppose the weight of the table is 23.4 N, the weight of each magnet is 2.67 N, and the magnetic force on the lower magnet is 5.71 times its weight. Find the magnitude of the force of the lower magnet on the upper magnet.

To find the magnitude of the force of the lower magnet on the upper magnet, we need to use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.

Given that the magnetic force on the lower magnet is 5.71 times its weight, we can calculate the weight of the lower magnet using the given weight of the table:

Weight of the table = 23.4 N
Weight of each magnet = 2.67 N (Assuming both magnets have the same weight)

Total weight of the magnets = 2 * 2.67 N = 5.34 N

Now, we can find the weight of the lower magnet (let's call it W_lower) by dividing the total weight of the magnets by the sum of the coefficients in the ratio:

W_lower = 5.34 N / (1 + 5.71) = 5.34 N / 6.71 = 0.796 N

Since the magnetic force on the lower magnet is 5.71 times its weight, we can calculate the magnitude of the force of the lower magnet on the upper magnet by multiplying the weight of the lower magnet by the coefficient:

Force of lower magnet on upper magnet = 0.796 N * 5.71 = 4.55 N (rounded to two decimal places)

Therefore, the magnitude of the force of the lower magnet on the upper magnet is approximately 4.55 N.

To find the magnitude of the force of the lower magnet on the upper magnet, we need to consider the forces acting on the lower magnet.

Let's break down the forces acting on the lower magnet:

1. Weight of the lower magnet: This force is pulling the lower magnet downwards and has a magnitude of 2.67 N.

2. Long-range attractive force: This is the force between the two magnets that keeps the lower magnet in place. It is given that the magnetic force on the lower magnet is 5.71 times its weight. Therefore, the magnetic force is 5.71 * 2.67 N.

To find the net force on the lower magnet, we need to subtract the weight of the lower magnet from the magnetic force:

Net force on the lower magnet = Magnetic force - Weight of lower magnet
= (5.71 * 2.67) N - 2.67 N

Now, calculating the net force:

Net force on the lower magnet = 15.2957 N - 2.67 N
= 12.6257 N

Since the lower magnet is in equilibrium, the net force acting on it must be zero. Therefore, the magnitude of the force of the lower magnet on the upper magnet is equal in magnitude but opposite in direction to the net force on the lower magnet.

Magnitude of the force of the lower magnet on the upper magnet = 12.6257 N