A 305 kg piano slides 4.0 m down a 30° incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. The effective coefficient of kinetic friction is 0.40.
(a) Calculate the force exerted by the man.
(b) Calculate the work done by the man on the piano.
(c) Calculate the work done by the friction force.
(d) What is the work done by the force of gravity?
(e) What is the net work done on the piano?
Could you explain how to?
Sure! To find the answers to these questions, we can use the concepts of forces, work, and energy. Here is how you can calculate each part:
(a) The force exerted by the man:
The force exerted by the man is equal to the component of the weight of the piano parallel to the incline, plus the force of friction opposing its motion. The force of friction is given by the equation:
Friction force = coefficient of kinetic friction * normal force
The normal force is the component of the weight perpendicular to the incline, which can be calculated using:
Normal force = weight * cos(theta)
where theta is the angle of the incline. The weight of the piano is given by:
Weight = mass * gravitational acceleration
The gravitational acceleration is 9.8 m/s^2. Therefore, you can calculate the force exerted by the man as:
Force exerted by the man = (Weight * sin(theta)) + (Friction force)
(b) The work done by the man on the piano:
The work done is equal to the force exerted by the man multiplied by the distance moved, which is given as 4.0 m in this case.
Work done by the man = (Force exerted by the man) * (distance moved)
(c) The work done by the friction force:
The work done by the friction force is given by the equation:
Work done by friction force = (Friction force) * (distance moved)
(d) The work done by the force of gravity:
The work done by the force of gravity is equal to the component of the weight of the piano parallel to the incline, multiplied by the distance moved. This can be calculated as:
Work done by gravity force = (Weight * sin(theta)) * (distance moved)
(e) The net work done on the piano:
The net work done on the piano is the sum of the work done by all the forces acting on it. It can be calculated by adding the work done by the man, the work done by the friction force, and the work done by the force of gravity.
Net work done on the piano = (Work done by the man) + (Work done by friction force) + (Work done by gravity force)
By substituting the appropriate values for mass, angle, coefficient of kinetic friction, and distance, you can calculate each part using these equations.