A 280 kg piano slides 4.3 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. 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.
formula for each question??
Ffr= ukFn
To solve this problem, we need to use several formulas related to forces, work, and friction. Here are the relevant formulas for each question:
(a) The force exerted by the man:
In this case, the force exerted by the man is equal in magnitude but opposite in direction to the force of friction. The equation we can use is:
Force of Friction = Effective coefficient of kinetic friction * Normal Force
The normal force can be calculated as:
Normal Force = Mass * Gravity * cos(θ)
where:
- Mass is the mass of the piano (280 kg),
- Gravity is the acceleration due to gravity (9.8 m/s^2), and
- θ is the angle of the incline (30°).
(b) The work done by the man on the piano:
The work done by a constant force parallel to the direction of motion is calculated using the equation:
Work = Force * Displacement * cos(θ)
where:
- Force is the force exerted by the man,
- Displacement is the distance the piano slides down the incline (4.3 m), and
- θ is the angle between the force vector and the displacement vector (since they are parallel, cos(θ)=1).
(c) The work done by the friction force:
The work done by the friction force can be calculated using the equation:
Work = Force of Friction * Displacement * cos(180°)
Since the displacement is downward and the frictional force opposes the motion, cos(180°)=-1.
(d) The work done by the force of gravity:
The work done by the force of gravity can be calculated using the equation:
Work = Force of Gravity * Displacement * cos(180°)
Since the displacement is downward and the gravitational force acts vertically downward, cos(180°)=-1.
(e) The net work done on the piano:
The net work done on an object is equal to the sum of the individual works done on it. Therefore, we can calculate it by adding the work done by the man (b), work done by the friction force (c), and work done by the force of gravity (d).
Now, let's solve each part using the given values.
How do you find friction force
So it is moving, but not accelerating. The kinetic friction force PLUS the man's applied force (f) balances the component of weight down the ramp.
For part (a)
f + 280*g*cos30*0.40 = 280*g*sin 30
Solve for f
(b) -f*4.3 m = _ J
(c) -(friction force)*4.3 =
(d) M g sin 30 * 4.3 =
(e) zero. The piano's KE does not increase.