Physics problem about nonconservative forces

Question

A 20.0-kg child descends a slide 2.30 m high and reaches the bottom with a speed of 1.45 m/s. How much thermal energy due to friction was generated in this process?

Answer 1

Energy is always conserved, which means that the total energy of the child will be equal to the gravitational potential energy (PE) at the top of the slide. As the child slides down, some of this energy is converted into kinetic energy (KE) and some into thermal energy due to friction. This means:

PE(top of slide) = KE(bottom of slide) + Thermal Energy

Calculate the Potential Energy at the Top

PE = mgh

1. m = mass (20.0 kg)
2. g = gravity (9.81 m/s²)
3. h = height (2.30 m)

Calculate the Kinetic Energy at the Bottom

KE = (1/2) mv²

1. v = speed at the bottom (1.45 m/s)

Find Thermal Energy

Solve for the thermal energy:

Thermal Energy = PE - KE

plug in the values to find your answer

Answer 2

First Method: Mechanic Energy Theorem : Delta(Em) = Work of non conservative forces

Em (bottom) - Em (top) = W(friction) with Em = Ek + Ep = 0.5xmxv² + mxgxh

(0.5x20.0x(1.45)² + 20.0x9.81x0) - (0.5x20.0x(0)² + 20.0x9.81x2.30) = W(friction)

So: W(friction) = - 430 J < 0 because energy is lost with friction.

Second Method: Kinetic Energy Theroem : Delta(Ek) = Work of all forces (conservative and non conservative forces)

Ek (bottom) - Ek (top) = W(weight) + W(friction) with Ek = 0.5xmxv² and W(weight) = + mxgxh because the child slides down

(0.5x20.0x(1.45)²) - (0.5x20.0x(0)²) = +20.0x9.81x2.30 + W(friction)

So: W(friction) = (0.5x20.0x(1.45)²) - (20.0x9.81x2.30) = - 430 J < 0 because energy is lost with friction.

I prefer this second one which is more powerful.