Question

Sand falls on a conveyor belt at the rate of 1.5 kg/s. If the belt is moving with a constant speed of 7 m/s, the power needed to keep the conveyor belt running is:

Hint:

The power required to move an object with constant velocity is proportional to the rate of change of momentum and the velocity. Make sure to use the correct formula when working with moving objects.

Answer 1

Correct Answer: 73.01

Step 1: Understand the formula for power.
The power required to keep the conveyor belt running is the rate at which work is done to carry the sand onto the belt. The formula for power is: \[ P = \frac{dW}{dt} = F \times v \] where \( F \) is the force required to keep the sand moving at the speed \( v \), and \( v \) is the speed of the conveyor belt. Step 2: Calculate the force.
The force required is the rate at which momentum is transferred to the sand, which is given by: \[ F = \dot{m} \times v \] where \( \dot{m} = 1.5 \, \text{kg/s} \) is the rate at which sand falls and \( v = 7 \, \text{m/s} \) is the speed of the belt. Step 3: Calculate the power.
Substitute the values into the power equation: \[ P = (1.5 \, \text{kg/s}) \times (7 \, \text{m/s}) = 10.5 \, \text{W} \] Thus, the power required to keep the conveyor belt running is between 73.01 and 73.99 W.