A 7159 N piano is to be pushed up a(n) 2.26 m
frictionless plank that makes an angle of 25.6
◦
with the horizontal.
Calculate the work done in sliding the piano
up the plank at a slow constant rate.
Answer in units of J.
distance up = 2.26 sin 25.6
work = m g h = 7159 * 2.26 sin 25.6
To calculate the work done in sliding the piano up the plank, we need to find the vertical component of the force applied to the piano and multiply it by the distance the piano is moved.
First, let's find the vertical component of the force applied to the piano. This can be done by finding the force component parallel to the incline.
The force parallel to the incline can be found using the formula:
Force parallel = Force applied * sin(angle)
where the angle is the angle of the incline measured from the horizontal and the Force applied is the given force of 7159 N.
Calculating the force parallel:
Force parallel = 7159 N * sin(25.6°)
Force parallel = 7159 N * 0.43297
Force parallel ≈ 3097.18 N
Now, we can calculate the work done by multiplying the force parallel by the distance the piano is moved.
Work done = Force parallel * distance
Work done = 3097.18 N * 2.26 m
Work done ≈ 7002.9 J
Therefore, the work done to slide the piano up the plank at a slow constant rate is approximately 7002.9 J.