An electric motor is rated to have a maximum power output of 0.72 hp. If this motor is being used to lift a crate of mass 188 kg, how fast (i.e., at what speed) can it lift the crate? Hint: Assume the only other force on the crate is the force of gravity.

0.72 hp =536.9 W

P = m•g•v
v =P/mg = 536.9/188•9.8 =0.29 m/s.

To determine the speed at which the motor can lift the crate, we need to calculate the force required to counteract gravity and then convert it into the speed at which the crate can be lifted. Here are the steps to solve the problem:

Step 1: Convert the horsepower to watts.
1 horsepower (hp) is equal to 746 watts. Therefore, we have:
0.72 hp * 746 W/hp = 536.32 W

Step 2: Calculate the force required to counteract gravity.
The force required to counteract gravity can be computed using the equation:
force = mass * acceleration due to gravity
force = 188 kg * 9.8 m/s^2 = 1842.4 N

Step 3: Determine the velocity using the power equation.
The power equation for an electric motor is given by:
power = force * velocity
Therefore, to solve for velocity, we rearrange the equation:
velocity = power / force
velocity = 536.32 W / 1842.4 N
velocity ≈ 0.291 m/s

So, the motor can lift the crate at a speed of approximately 0.291 m/s.

To find the speed at which the motor can lift the crate, we need to calculate the force applied by the motor.

First, let's convert the power rating from horsepower (hp) to watts (W).

1 hp = 746 watts

So, the motor's power output is:
0.72 hp * 746 W/hp = 536.32 W

Now, let's calculate the force applied by the motor to lift the crate. The force is equal to the power divided by the speed:

Force (F) = Power (P) / Speed (v)

We know the power (536.32 W), and we need to find the force. The only other force acting on the crate is the force of gravity.

The force of gravity is given by:
Force of gravity = mass * acceleration due to gravity

The mass of the crate is given as 188 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.

Force of gravity = 188 kg * 9.8 m/s^2 = 1842.4 N

Since there are no other forces acting on the crate, the force applied by the motor must be equal to the force of gravity.

Therefore, Force (F) = 1842.4 N

Now, we can rearrange the equation to solve for speed:

Speed (v) = Power (P) / Force (F)

Speed (v) = 536.32 W / 1842.4 N

Calculating this value gives us the speed at which the motor can lift the crate.