A 2302 kg block of granite is pulled up an incline that has an angle of inclination of 17.0 o with a constant speed of 2.22 m/s by a steam winch (see Figure). The coefficient of kinetic friction between the block and the incline is 0.340. How much power must be supplied by the winch?
Power is Work/Time, or Force*Distance/Time.
You have a velocity, which is Distance over time, so you need to find the force that the winch needs to pull the block upwards. That force is the frictional force (coefficient of friction* normal force) + the force of gravity down the ramp.
After you get the force, times it by the velocity to get the power.
To calculate the power supplied by the winch, we need to consider the forces acting on the block:
1. Gravitational force (weight):
The weight of the granite block can be calculated using the formula: weight = mass * gravitational acceleration.
Given that the mass of the block is 2302 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight: weight = 2302 kg * 9.8 m/s^2.
2. Normal force:
The normal force is the force exerted by the incline on the block perpendicular to the surface. On an inclined plane, the normal force can be calculated using the formula: normal force = weight * cos(angle of inclination).
Given that the angle of inclination is 17.0 degrees, we can calculate the normal force: normal force = weight * cos(17.0).
3. Friction force:
The friction force can be calculated using the formula: friction force = coefficient of kinetic friction * normal force.
Given that the coefficient of kinetic friction is 0.340 and we have already calculated the normal force, we can calculate the friction force: friction force = 0.340 * normal force.
Since the block is moving up the incline at a constant speed, the force applied by the winch must exactly balance the gravitational force and the friction force. Therefore, the total force acting on the block is the sum of the weight and the friction force.
Finally, to calculate the power supplied by the winch, we use the formula: power = force * velocity.
By plugging in the values we have calculated into the formula, we can find the answer to the question.