A 4.2-kilogram block sliding down a ramp from a height of 4.5 meters above the ground reaches the ground with a kinetic energy of 33 joules. The total work done by friction on the block as it slides down the ramp is approximately:
To find the total work done by friction on the block, we first need to calculate the potential energy of the block when it is at the top of the ramp.
The potential energy (PE) of an object is calculated using the formula PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the object.
Given:
Mass of the block (m) = 4.2 kg
Height of the ramp (h) = 4.5 m
Now we can calculate the potential energy:
PE = m * g * h
= 4.2 kg * 9.8 m/s² * 4.5 m
≈ 183.33 joules
The potential energy at the top of the ramp is approximately 183.33 joules. This is the amount of energy the block has before it starts sliding down the ramp.
Next, we find the change in energy as the block slides down the ramp. This is the difference between the potential energy at the top of the ramp and the kinetic energy at the bottom.
Change in energy = Potential energy at top - Kinetic energy at bottom
= 183.33 joules - 33 joules
= 150.33 joules
The change in energy represents the work done by the force of gravity on the block as it slides down the ramp. But since the kinetic energy is equal to the work done by all forces acting on the block, we can conclude that the remaining work is done by friction.
Therefore, the total work done by friction on the block as it slides down the ramp is approximately 150.33 joules.