# A 284 kg crate is pulled along a level surface by an engine. The coefficient of kinetic friction between the crate and the surface is 0.513. How much power must the engine deliver to move the crate at a constant speed of 7.2 m/s?

## M*g = 284kg * 9.8N./kg = 2783.2 N. = Wt. of the crate = Normal force(Fn).

Fk = u*Fn = 0.513 * 2783.2 = 1427.8 N. =
Force of kinetic friction.

Fap-Fk = M*a
Fap-1427.8 = M*0 = 0
Fap = 1427.8 N. = Force applied.

Power = Fap * V = 1427.8 * 7.2 = 10,280
J/s. = 10,280 Watts.

## To determine how much power the engine must deliver to move the crate at a constant speed, we can use the equation P = F x v, where P is the power, F is the force, and v is the velocity.

First, we need to find the force exerted on the crate. The force can be calculated using the equation F = μN, where μ is the coefficient of kinetic friction and N is the normal force.

To find the normal force, we can use the equation N = mg, where m is the mass of the crate and g is the acceleration due to gravity.

Given that the mass of the crate is 284 kg, the acceleration due to gravity is approximately 9.8 m/s².

N = (284 kg)(9.8 m/s²)
N = 2783.2 N

Now, we can calculate the force:

F = (0.513)(2783.2 N)
F ≈ 1428.9 N

Finally, we can determine the power:

P = (1428.9 N)(7.2 m/s)
P ≈ 10283.28 W

Therefore, the engine must deliver approximately 10283.28 watts of power to move the crate at a constant speed of 7.2 m/s.

## To calculate the power required to move the crate at a constant speed, we first need to determine the force required to overcome the friction.

The formula to calculate the force of friction is:

Friction force = coefficient of friction × normal force

The normal force can be calculated by multiplying the mass of the crate by the acceleration due to gravity. In this case, the normal force will be:

Normal force = mass × acceleration due to gravity
= 284 kg × 9.8 m/s^2

Next, we can calculate the force of friction:

Friction force = coefficient of friction × normal force
= 0.513 × (284 kg × 9.8 m/s^2)

Now, we have the force of friction acting against the crate's motion. Since the crate is moving at a constant speed, there is no net force acting in the horizontal direction. Therefore, the force applied by the engine must be equal to the force of friction:

Force applied by engine = force of friction

Finally, we can calculate the power required using the formula:

Power = force × velocity
= Force applied by engine × velocity
= (0.513 × 284 kg × 9.8 m/s^2) × 7.2 m/s

Plug in the values and calculate to find the required power.