A 17 kg child descends a slide 3.5 m high and reaches the bottom with a speed of 1.5 m/s. How much work was done by the friction as the child goes down the slide?

Pe lost = m g h

Ke gained = (1/2) m v^2

Pe lost - Ke gained = energy lost to friction

To find the work done by friction as the child goes down the slide, we first need to calculate the gravitational potential energy at the top of the slide and the kinetic energy at the bottom. By using the work-energy principle, we can determine the work done by friction.

1. Calculate the gravitational potential energy at the top of the slide:
The gravitational potential energy (GPE) can be calculated using the formula: GPE = mgh, where m is the mass (17 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the slide (3.5 m).

GPE = (17 kg) × (9.8 m/s²) × (3.5 m)
= 588.7 Joules (J)

So, the gravitational potential energy at the top of the slide is 588.7 J.

2. Calculate the kinetic energy at the bottom of the slide:
The kinetic energy (KE) can be calculated using the formula: KE = 0.5mv², where m is the mass (17 kg) and v is the velocity (1.5 m/s).

KE = 0.5 × (17 kg) × (1.5 m/s)²
= 19.125 Joules (J)

So, the kinetic energy at the bottom of the slide is 19.125 J.

3. Find the work done by friction:
According to the work-energy principle, the work done by friction is equal to the change in mechanical energy, which is the difference between the gravitational potential energy at the top and the kinetic energy at the bottom.

Work done by friction = GPE - KE
= 588.7 J - 19.125 J
= 569.575 Joules (J)

Therefore, the work done by friction as the child goes down the slide is approximately 569.575 J.