A 3.9-kilogram block sliding down a ramp from a height of 5.2 meters above the ground reaches the ground with a kinetic energy of 36 joules. The total work done by friction on the block as it slides down the ramp is approximately

work done by gravity= frictionwork+KE

3.9g*5.2=36+frictionwork

To find the total work done by friction on the block as it slides down the ramp, we can use the work-energy theorem.

The work-energy theorem states that the work done on an object equals the change in its kinetic energy.

In this case, the initial potential energy of the block when it is at a height of 5.2 meters above the ground is given by:

Potential Energy = mass * gravity * height
Potential Energy = 3.9 kg * 9.8 m/s^2 * 5.2 m
Potential Energy = 202.416 J

Given that the final kinetic energy of the block is 36 joules, we can now calculate the work done by friction.

Work Done by Friction = Final Kinetic Energy - Initial Potential Energy
Work Done by Friction = 36 J - 202.416 J
Work Done by Friction ≈ -166.42 J

Note that the negative sign indicates that the work done by friction is in the opposite direction of the displacement of the block. In this case, the friction force causes a loss of energy, hence the negative sign.

Therefore, the total work done by friction on the block as it slides down the ramp is approximately -166.42 joules.

To find the total work done by friction on the block as it slides down the ramp, we need to calculate the change in the gravitational potential energy of the block and subtract the kinetic energy at the end.

First, let's calculate the change in potential energy of the block. The potential energy is given by the equation:

Potential Energy = mass * gravity * height

where:
mass = 3.9 kilograms
gravity = 9.8 meters per second squared (acceleration due to gravity)
height = 5.2 meters

So, the potential energy is:
Potential Energy = 3.9 kg * 9.8 m/s^2 * 5.2 m

Next, we need to calculate the work done by friction. The work done by a force can be calculated using the equation:

Work = force * distance * cosine(theta)

The force of friction can be calculated using the equation:

Force of friction = coefficient of friction * normal force

where:
coefficient of friction is the ratio of the force of friction to the normal force, and
normal force is equal to the weight of the object, which is m * g (mass * acceleration due to gravity)

We need the coefficient of friction to calculate the force of friction. Let's assume a coefficient of friction for now.

Finally, we need the distance over which friction acts. As the block slides down the ramp, the distance is equal to the length of the ramp. However, the length of the ramp is not provided, so we cannot calculate the exact work done by friction without this information. We can only approximate it.

To approximate the work done by friction, we can assume that the friction acts over the entire height of the ramp. So, the distance over which friction acts is equal to the height of the ramp, which is 5.2 meters.

Now, let's calculate the work done by friction using the information we have:

Work = force of friction * distance * cosine(theta)

Since the block is sliding downward, the angle between the force of friction and the displacement is 180 degrees, so the cosine(theta) is -1.

Substituting the values we have:
Work = force of friction * 5.2 m * -1

So, to get the total work done by friction, we need to know the coefficient of friction and the length of the ramp. Once we have these values, we can substitute them into the equation above to get the answer.