A 20 g fridge magnet is being held onto the fridge by a 0.9 N force. coefficient of kinetic friction is 0.3 . (please include an FBD when giving the solutions)

Question

a. calculate the friction acting on the magnet.

b. calculate the weight of the magnet

c.the acceleration of the magnet.

please explain along the way

Bot · Answer

First, let's draw the Free Body Diagram (FBD) of the forces acting on the fridge magnet.

There are three main forces acting on the magnet.

1. The gravitational force (weight) acting vertically downwards, denoted as W.
2. The force holding the magnet onto the fridge, acting vertically upwards, denoted as F (given as 0.9 N).
3. The frictional force acting horizontally to oppose the motion of the magnet, denoted as F_friction.

The gravitational force (W) can be calculated as:
W = m * g
where m is the mass of the magnet (0.020 kg, converted from 20g) and g is the acceleration due to gravity (approximately 9.81 m/s^2).

W = 0.020 * 9.81 = 0.1962 N

Now that we have the weight of the magnet, we can move on to part (a).

a) Calculate the friction acting on the magnet.

To find the frictional force, we need to use the formula:
F_friction = μ * N
where μ is the coefficient of kinetic friction (0.3) and N is the normal force.

In this case, the normal force (force perpendicular to the surface) is equal to the force holding the magnet onto the fridge (the 0.9 N force). This is because the magnet is in equilibrium in the vertical direction (it's not moving up or down).

F_friction = 0.3 * 0.9 = 0.27 N

For part (b), we already calculated the weight of the magnet above:

The weight of the magnet, W = 0.1962 N.

For part (c), we need to find the acceleration of the magnet.

As the magnet is in equilibrium in the vertical direction, we only need to consider forces in the horizontal direction. Newton's second law states that:

F_net = m * a,
where F_net is the net force acting on the object, m is the mass, and a is the acceleration.

Since the only force acting horizontally is the frictional force, and it is opposing the direction of the movement of the magnet:

F_net = -F_friction = -0.27 N

Now we can calculate the acceleration:

a = F_net / m = -0.27 / 0.020 = -13.5 m/s²

The acceleration of the magnet is -13.5 m/s², indicating that it is decelerating due to the frictional force.

In summary,

a) The frictional force acting on the magnet is 0.27 N.
b) The weight of the magnet is 0.1962 N.
c) The acceleration of the magnet is -13.5 m/s².