To solve this problem, we first need to calculate the work done by the crane. The work done (W) is given by the formula:

W = m * g * h

where:
m = mass of the concrete block = 120 kg
g = acceleration due to gravity = 9.8 m/s²
h = height = 10 m

Substituting these values into the formula, we get:

W = 120 kg * 9.8 m/s² * 10 m = 11760 Joules

Next, we calculate the power output of the crane. Power (P) is work done per unit time, so:

P = W / t

where:
W = work done = 11760 Joules
t = time = 6 s

Substituting these values into the formula, we get:

P = 11760 Joules / 6 s = 1960 Watts = 1.96 kW

The efficiency (η) of the motor is the ratio of the power output to the power input, expressed as a percentage. So:

η = (Power output / Power input) * 100%

Substituting the given and calculated values into the formula, we get:

η = (1.96 kW / 3 kW) * 100% = 65.33%

So, the efficiency of the motor is approximately 65.33%.

Question

To solve this problem, we first need to calculate the work done by the crane. The work done (W) is given by the formula:

W = m * g * h

where:
m = mass of the concrete block = 120 kg
g = acceleration due to gravity = 9.8 m/s²
h = height = 10 m

Substituting these values into the formula, we get:

W = 120 kg * 9.8 m/s² * 10 m = 11760 Joules

Next, we calculate the power output of the crane. Power (P) is work done per unit time, so:

P = W / t

where:
W = work done = 11760 Joules
t = time = 6 s

Substituting these values into the formula, we get:

P = 11760 Joules / 6 s = 1960 Watts = 1.96 kW

The efficiency (η) of the motor is the ratio of the power output to the power input, expressed as a percentage. So:

η = (Power output / Power input) * 100%

Substituting the given and calculated values into the formula, we get:

η = (1.96 kW / 3 kW) * 100% = 65.33%

So, the efficiency of the motor is approximately 65.33%.

Knowee AI · Accepted Answer

To solve this problem, we first need to calculate the work done by the crane. The work done (W) is given by the formula:

W = m * g * h

where:
m = mass of the concrete block = 120 kg
g = acceleration due to gravity = 9.8 m/s²
h = height = 10 m

Substituting these values into the formula, we get:

W = 120 kg * 9.8 m/s² * 10 m = 11760 Joules

Next, we calculate the power output of the crane. Power (P) is work done per unit time, so:

P = W / t

where:
W = work done = 11760 Joules
t = time = 6 s

Substituting these values into the formula, we get:

P = 11760 Joules / 6 s = 1960 Watts = 1.96 kW

The efficiency (η) of the motor is the ratio of the power output to the power input, expressed as a percentage. So:

η = (Power output / Power input) * 100%

Substituting the given and calculated values into the formula, we get:

η = (1.96 kW / 3 kW) * 100% = 65.33%

So, the efficiency of the motor is approximately 65.33%.

A crane lifts a 120 kg block of concrete through a vertical height of 10 m in 6 s. If the power supplied to the motor driving the crane is 3 kW, what is the efficiency of the motor?