A physics student uses a ramp to slide a 350 kg piano onto the back of a pickup truck. The box on the back of the truck is 81 cm above the ground and the planks are 3 m long. An average force of 1500 N is required to slide the piano up the planks.
a) Determine the work done in loading the piano.
b) Calculate the work done by friction.
a) f * d = 1500 N * 3 m = 4500 J
b) 4500 J - m g h = 4500 J - (350 kg * 9.8 m/s^2 * .81 m)
To solve these questions, we first need to understand the work-energy principle in physics. According to this principle, the work done on an object is equal to the change in its kinetic energy.
a) To determine the work done in loading the piano, we need to calculate the change in its gravitational potential energy as it is lifted onto the truck. The formula for gravitational potential energy is given by:
Potential Energy = mass * acceleration due to gravity * height
Given that the mass of the piano (m) is 350 kg, the height (h) is 81 cm, and the acceleration due to gravity (g) is approximately 9.8 m/s^2, we can plug in these values to calculate the potential energy:
Potential Energy = 350 kg * 9.8 m/s^2 * 0.81 m
Now, multiplying these values, we get:
Potential Energy = 2718.9 J
Therefore, the work done in loading the piano is approximately 2718.9 Joules.
b) To calculate the work done by friction, we need to understand that work against friction is equal to the force of friction multiplied by the distance over which it acts. The formula for work done is given by:
Work = force * distance * cosine(angle)
In this case, the force of friction is equal to the force required to slide the piano up the planks, which is given as 1500 N. The distance is given as 3 m, which is the length of the planks. The angle between the force and the direction of motion is usually assumed to be 0 degrees, so the cosine(angle) becomes 1.
Plugging in these values, we get:
Work = 1500 N * 3 m * 1
Therefore, the work done by friction is 4500 Joules.