A 255 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 (Fig. 6-35). 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?
force man+forcefrition=weightdownplane
forceman=mgSinTheta-mg*mu*cosTheta
work done=force*distance.
(c) Calculate the work done by the friction force.
-3937.6J
(d) What is the work done by the force of gravity?
5684J
(e) What is the net work done on the piano?
0J (zeroJ)
don't know A & b yet! sorry
this anwer was for a 290kg piano..ma bad!
To answer these questions, we need to break down the problem and use the relevant formulas. Let's go step by step:
(a) To calculate the force exerted by the man, we can use the equation:
ΣF = m * a
In this case, the net force (ΣF) is equal to the force exerted by the man. The mass (m) is given as 255 kg. The acceleration (a) of the piano along the incline can be calculated using the formula:
a = g * sin(θ)
where g is the acceleration due to gravity (9.8 m/s^2) and θ is the angle of the incline (30° in this case).
Once we have the acceleration, we can substitute the values into the first equation to find the force exerted by the man.
(b) To calculate the work done by the man on the piano, we can use the equation:
Work = Force * Distance * cos(θ)
Here, the force is the force exerted by the man (calculated in part (a)), the distance is the distance the piano slides down the incline (given as 4.3 m), and θ is the angle of the incline (30°).
(c) To calculate the work done by the friction force, we can use the equation:
Work = Force of friction * Distance
The force of friction can be calculated using the formula:
Force of friction = μ * N
where μ is the coefficient of kinetic friction (given as 0.40). The normal force (N) can be calculated using:
N = m * g * cos(θ)
Once we have the force of friction, we can substitute the values into the second equation to find the work done by the friction force.
(d) The work done by the force of gravity can be calculated using the equation:
Work = Force * Distance * cos(180°)
Here, the force is the weight of the piano, which is equal to its mass multiplied by the acceleration due to gravity (m * g). The distance is the same distance the piano slides down the incline (4.3 m). The cosine of 180° is -1, as the force of gravity acts opposite to the direction of motion.
(e) The net work done on the piano can be calculated by summing up the work done by the man, the work done by the friction force, and the work done by the force of gravity.
I hope this explanation helps you understand how to approach and solve the problem. Let me know if you have any further questions!