A 380- piano slides 3.8 down a 22 incline and is kept from accelerating by a man who is pushing back on it parallel to the incline.

a.Determine the force exerted by the man.
b.Determine the work done by the man on the piano.
c.Determine the work done by the force of gravity.
d.Determine the net work done on the piano. Ignore friction.

a)As the acceleration is zero, the force exerted by the man equal the comp. of gravitational force on the body along the incline.

F = mg*Sin22
b)Wm = F.d
= - 3.8*F ( -ve because F and d are in opposite directions)
c) Wg = +3.8*mg*Sin22
d) Net force on piano = 0. So Wnet = 0

post it.

a. The force exerted by the man can be calculated using the formula F = m * a, where F is the force, m is the mass, and a is the acceleration. Since the piano is not accelerating, the force exerted by the man must be equal to the force of gravity acting on the piano. Therefore, the force exerted by the man is equal to the weight of the piano, which can be calculated as F = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). So, the force exerted by the man is 380 kg * 9.8 m/s^2.

b. The work done by the man on the piano can be calculated using the formula W = F * d * cos(θ), where W is the work done, F is the force, d is the distance, and θ is the angle between the force and the displacement. Since the force exerted by the man is parallel to the incline, the angle θ is 0 degrees. The distance the piano slides down the incline is given as 3.8 m. Putting these values into the formula, we can calculate the work done by the man.

c. The work done by the force of gravity can be calculated using the formula W = m * g * d * cos(θ). In this case, the force of gravity acts vertically downward, while the displacement is along the incline. Therefore, the angle θ is 90 degrees. Putting the values into the formula, we can calculate the work done by the force of gravity.

d. The net work done on the piano is the sum of the work done by the man and the work done by the force of gravity. Therefore, to calculate the net work done on the piano, we add the work done by the man and the work done by the force of gravity.

To answer these questions, we need to understand the concepts of force, work, and inclined planes.

First, let's address part a. To determine the force exerted by the man, we need to consider the forces acting on the piano. The force exerted by the man must be equal in magnitude and opposite in direction to the force of gravity acting on the piano. This is because the piano is kept from accelerating, meaning the net force on it is zero.

The force of gravity can be calculated by multiplying the mass of the piano (380 kg) by the acceleration due to gravity (9.8 m/s^2). So the force of gravity acting on the piano is (380 kg) * (9.8 m/s^2) = 3724 N.

Since the force exerted by the man is equal in magnitude but opposite in direction, the force exerted by the man is also 3724 N.

Moving on to part b, to determine the work done by the man on the piano, we need to use the formula:

Work = Force * Distance * cosθ

Where:
- Force is the force exerted by the man (3724 N),
- Distance is the distance the piano slides down the incline (3.8 m), and
- θ is the angle between the force vector and the displacement vector (in this case, parallel to the incline, so θ = 0°).

Plugging the values into the formula, the work done by the man is (3724 N) * (3.8 m) * cos(0°) = 14135.2 J (Joules).

For part c, the work done by the force of gravity can also be calculated using the same formula:

Work = Force * Distance * cosθ

Where:
- Force is the force of gravity acting on the piano (3724 N),
- Distance is the distance the piano slides down the incline (3.8 m), and
- θ is the angle between the force vector and the displacement vector (in this case, parallel to the incline, so θ = 0°).

Plugging the values into the formula, the work done by the force of gravity is (3724 N) * (3.8 m) * cos(0°) = 14135.2 J.

Lastly, for part d, the net work done on the piano is the sum of the work done by the man and the work done by the force of gravity. Since both values are the same (14135.2 J), the net work done on the piano is 2 * 14135.2 J = 28270.4 J.

To recap:
a. The force exerted by the man is 3724 N.
b. The work done by the man on the piano is 13135.2 J.
c. The work done by the force of gravity is 14135.2 J.
d. The net work done on the piano is 28270.4 J.