A mass m = 1 kg initially at rest at height h = 2m slides to the bottom of a 45 ramp. there is no friction between the mass and the ramp. At the bottom of the ramp the speed of the mass is 4 m/s. How much heat was generated by the friction as the mass slides down the ramp?

Question

A mass m = 1 kg initially at rest at height h = 2m slides to the bottom of a 45 ramp. there is no friction between the mass and the ramp. At the bottom of the ramp the speed of the mass is 4 m/s. How much heat was generated by the friction as the mass slides down the ramp?

Any help? I'm very confused

Answer 1

final energy=orig PE -friction

1/2 m 4^2=m*g*2-friction heat

solve for friction heat.

Answer 2

Thank you so much for the help!!

Just to double check my math is correct, did you get about 2J as your answer? 2.45 to be exact

Answer 3

quick check using 10 for g

8 = 20 - heat
heat is about 12

Answer 4

To find the amount of heat generated by friction as the mass slides down the ramp, we first need to understand the concept of work done against friction.

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done against friction will be converted into heat energy.

Here's how we can calculate the work done against friction:

1. Calculate the initial potential energy:
The initial potential energy of the mass can be calculated using the formula:
Potential energy (initial) = mass * gravity * height
Potential energy (initial) = 1 kg * 9.8 m/s^2 * 2 m

2. Calculate the final kinetic energy:
The final kinetic energy of the mass can be calculated using the formula:
Kinetic energy (final) = 0.5 * mass * velocity^2
Kinetic energy (final) = 0.5 * 1 kg * (4 m/s)^2

3. Calculate the work done against friction:
Since there is no friction between the mass and the ramp, the work done against friction is zero because no energy is lost due to friction.

4. Calculate the change in mechanical energy:
Change in mechanical energy = Kinetic energy (final) - Potential energy (initial)
Change in mechanical energy = (0.5 * 1 kg * (4 m/s)^2) - (1 kg * 9.8 m/s^2 * 2 m)

5. Calculate the amount of heat generated:
The amount of heat generated is equal to the change in mechanical energy since no other forms of energy are involved.
Heat generated = Change in mechanical energy

Therefore, to find the amount of heat generated by friction as the mass slides down the ramp, you need to calculate the change in mechanical energy using the formulas mentioned above. In this case, the change in mechanical energy would be the amount of heat generated.