A 3.3-kilogram block sliding down a ramp from a height of 4.5 meters above the ground reaches the ground with a kinetic energy of 35 joules. The total work done by friction on the block as it slides down the ramp is approximately: [1 d.p.]
To find the total work done by friction on the block as it slides down the ramp, we need to calculate the change in mechanical energy of the block.
The mechanical energy of an object is the sum of its potential energy and kinetic energy. In this case, the potential energy is given by the equation:
Potential Energy = mass * gravity * height
where mass is the mass of the block (in kilograms), gravity is the acceleration due to gravity (approximately 9.8 m/s²), and height is the height of the ramp (in meters).
In this problem, the mass of the block is 3.3 kilograms and the height of the ramp is 4.5 meters. Thus, the potential energy of the block at the top of the ramp is:
Potential Energy = 3.3 kg * 9.8 m/s² * 4.5 m
= 144.27 joules
Since the total work done on an object is equal to the change in its mechanical energy, we can calculate the work done by friction using the equation:
Work done by friction = Change in mechanical energy
= Final mechanical energy - Initial mechanical energy
The final mechanical energy is given by the kinetic energy of the block at the bottom of the ramp, which is 35 joules.
So, the work done by friction is:
Work done by friction = 35 joules - 144.27 joules
= -109.27 joules (rounded to 1 decimal place)
Note that the negative sign indicates that the work done by friction is in the opposite direction of the motion of the block.