A 3.6-kilogram block sliding down a ramp from a height of 4.6 meters above the ground reaches the ground with a kinetic energy of 37 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 first calculate the gravitational potential energy of the block at the top of the ramp.
The gravitational potential energy (PE) is given by the formula:
PE = mgh
where m is the mass of the block, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the ramp.
Substituting the given values:
PE = (3.6 kg)(9.8 m/s^2)(4.6 m)
PE = 162.288 J
Next, we can use the principle of conservation of energy to find the work done by friction. According to this principle, the total mechanical energy (the sum of the potential energy and kinetic energy) remains constant if no external forces act on the object.
The total mechanical energy (ME) is given by the equation:
ME = PE + KE
where KE is the kinetic energy of the block.
Substituting the given values:
ME = 162.288 J + 37 J
ME = 199.288 J
Since there are no external forces acting on the block, all the work done on the block is converted into kinetic energy. Therefore, the work done by friction can be found by subtracting the initial potential energy from the total mechanical energy:
Work done by friction = ME - PE
Work done by friction = 199.288 J - 162.288 J
Work done by friction ≈ 37 J
Hence, the approximate total work done by friction on the block as it slides down the ramp is 37 joules.