a 20 kg crate is initially moving down a wall at a speed of 2.0 m/s. Determine the magnitude of the average force exerted by the person in order to stop the crate's downward motion in a distance of .50 m. The person pushes in a direction 53 degrees above the horizontal, and the coefficient of friction between the crate and wall is .40. Can someone please help me??????

It is 180.88

To determine the magnitude of the average force exerted by the person to stop the crate's downward motion, we need to consider the following steps:

Step 1: Calculate the crate's initial kinetic energy.
The initial kinetic energy (K₁) of the crate can be calculated using the formula:
K₁ = (1/2) * m * v₁²

Where:
m = mass of the crate = 20 kg
v₁ = initial velocity of the crate = 2.0 m/s

Substituting the given values into the formula:
K₁ = (1/2) * 20 kg * (2.0 m/s)²
K₁ = 40 J

Step 2: Calculate the work done against gravity.
The work done against gravity (W_gas) can be calculated using the formula:
W_gas = m * g * h

Where:
m = mass of the crate = 20 kg
g = acceleration due to gravity = 9.8 m/s²
h = vertical displacement = -0.50 m (since it is moving downward)

Substituting the given values into the formula:
W_gas = 20 kg * 9.8 m/s² * (-0.50 m)
W_gas = -98 J

Note: The negative sign indicates that the work is done against the downward force of gravity.

Step 3: Calculate the work done against friction.
The work done against friction (W_friction) can be calculated using the formula:
W_friction = μ * N * d

Where:
μ = coefficient of friction = 0.40
N = normal force (equals to the weight of the crate) = m * g
d = horizontal displacement = -0.50 m (since it is moving downward)

Substituting the values into the formula:
N = 20 kg * 9.8 m/s²
N = 196 N

W_friction = 0.40 * 196 N * (-0.50 m)
W_friction = -39.2 J

Note: The negative sign indicates that the work is done against the force of friction.

Step 4: Calculate the net work done on the crate.
The net work done on the crate (W_net) can be calculated by:
W_net = K₁ + W_gas + W_friction

Substituting the known values into the formula:
W_net = 40 J + (-98 J) + (-39.2 J)
W_net = -97.2 J

Step 5: Calculate the average force exerted by the person.
The average force exerted by the person (F_avg) can be calculated using the formula:
F_avg = W_net / d

Where:
W_net = net work done on the crate = -97.2 J
d = horizontal displacement = -0.50 m (since it is moving downward)

Substituting the known values into the formula:
F_avg = -97.2 J / (-0.50 m)
F_avg = 194.4 N

Therefore, the magnitude of the average force exerted by the person to stop the crate's downward motion in a distance of 0.50 m is 194.4 N.