a 330 kg piano slides 3.6 m down a 28 degree incline and is kept from accelerating by a man who is pushing back on it parallel to the incline. the effective coefficient of kinetic froction is 0.4. calculate
a) the force exerted by the man,
b)the work done by the man on the piano
c)the work done by the friction force
d) the work done by the force of gravity, and
e) the net work done on the piano.
To calculate these values, we can use the following formulas:
a) Force exerted by the man:
The force exerted by the man is equal in magnitude and opposite in direction to the force of friction. It can be calculated using the formula:
Force of friction = coefficient of kinetic friction x Normal force
First, let's calculate the normal force:
Normal force = mass x gravitational acceleration x cosine(angle of incline)
Normal force = 330 kg x 9.8 m/s^2 x cosine(28 degrees)
Now, we can calculate the force of friction:
Force of friction = coefficient of kinetic friction x Normal force
Force of friction = 0.4 x Normal force
b) Work done by the man on the piano:
Work done by a force is given by the formula:
Work = Force x distance
Since the force exerted by the man is parallel to the displacement, the work done by the man on the piano is simply:
Work done by the man = Force of friction x distance (3.6 m)
c) Work done by the friction force:
The work done by a friction force is given by the formula:
Work = Force of friction x distance
d) Work done by the force of gravity:
The work done by the force of gravity can be calculated as the product of the component of the force of gravity acting parallel to the displacement and the distance moved.
Force of gravity = mass x gravitational acceleration
Component of the force of gravity parallel to the incline = Force of gravity x sine(angle of incline)
Work done by the force of gravity = Component of the force of gravity parallel to the incline x distance (3.6 m)
e) Net work done on the piano:
The net work done on an object is the sum of all the individual works done on it. In this case, it is the sum of 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 = Work done by the man + Work done by the friction force + Work done by the force of gravity
Now that we have the formulas, we can plug in the values and calculate the answers.