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 calculate the initial potential energy of the block, the final kinetic energy of the block, and the work done by friction.

First, let's determine the initial potential energy (PE) of the block. The potential energy is given by the equation:

PE = mgh

where m is the mass of the block, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the ramp.

Given:
m = 3.6 kg
g = 9.8 m/s²
h = 4.6 m

Using the equation, we can calculate the initial potential energy:

PE = (3.6 kg) * (9.8 m/s²) * (4.6 m)
≈ 158.904 J

Next, we need to determine the final kinetic energy (KE) of the block. The kinetic energy is given by the equation:

KE = (1/2) * m * v²

where m is the mass of the block and v is the velocity of the block.

Given:
m = 3.6 kg
KE = 37 J

Rearranging the equation, we can solve for the velocity:

v = sqrt( (2 * KE) / m )
= sqrt( (2 * 37 J) / 3.6 kg )
≈ 3.250 m/s

Now, to find the work done by friction, we can use the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy. In this case, the frictional force does negative work, reducing the kinetic energy.

Therefore, the work done by friction is:

Work = KE_final - KE_initial
= 37 J - 0 J (initial kinetic energy is zero at the top of the ramp)
= 37 J

So, the total work done by friction on the block as it slides down the ramp is approximately 37 joules.