Dylan hangs a calendar on a refrigerator with a magnetic hook. Unfortunately, the magnet is too weak, so the magnet and calendar slide down the side of the refrigerator to the floor with an acceleration of magnitude 3ms2. If the coefficient of sliding friction between the magnet and the refrigerator is 0.1, what is the magnitude of the total vertical force the refrigerator exerts on the magnet? The mass of the magnet is 0.05kg and the mass of the calendar is 0.1kg. There is no contact between the calendar and the refrigerator.

I tried just calculating the m*a of the magnet-calendar system (=.45) thinking it would give me the net force in the y-direction but it was wrong.

Never mind, I got it

To solve this problem, we need to consider the forces acting on the magnet-calendar system separately in the horizontal and vertical directions.

First, let's analyze the forces in the horizontal direction. The only force acting on the magnet is the sliding friction force between the magnet and the refrigerator. This friction force can be calculated using the equation:

friction force = coefficient of sliding friction * normal force

Since there is no vertical contact between the calendar and the refrigerator, the normal force is equal to the weight of the magnet:

normal force = mass of the magnet * acceleration due to gravity
= 0.05 kg * 9.8 m/s^2
= 0.49 N

Now, the friction force can be calculated:

friction force = 0.1 * 0.49 N
= 0.049 N

Since the friction force is the only force acting in the horizontal direction, it is equal to the net horizontal force on the magnet:

net horizontal force = friction force
= 0.049 N

Next, let's analyze the forces in the vertical direction. The magnet is sliding vertically downward with an acceleration of 3 m/s^2. The only vertical force acting on the magnet is the normal force exerted by the refrigerator toward the magnet. This force can be calculated using the equation:

normal force = mass of the magnet * acceleration
= 0.05 kg * 3 m/s^2
= 0.15 N

Now, we need to find the total vertical force exerted by the refrigerator on the magnet. This force is the sum of the weight of the magnet and the normal force:

total vertical force = weight of the magnet + normal force
= mass of the magnet * acceleration due to gravity + normal force
= 0.05 kg * 9.8 m/s^2 + 0.15 N
= 0.49 N + 0.15 N
= 0.64 N

Therefore, the magnitude of the total vertical force the refrigerator exerts on the magnet is 0.64 N.

When attempting this problem, it seems you only considered the net force in the vertical direction. However, it is important to also analyze the forces in the horizontal direction separately to find the correct answer.