A 17 kg child descends a slide 3.5 m high and reaches the bottom with a speed of 4.5 m/s. How much work was done by friction as the child goes down the slide?

To find the work done by friction, we need to know the force of friction and the distance over which it acts.

The work done by friction can be calculated using the formula:

Work = Force x Distance

However, in this case, we don't have the force of friction directly. Instead, we can use the conservation of energy principle to find it.

The total mechanical energy of the child on the slide is conserved, meaning that the initial potential energy (due to height) is converted entirely into kinetic energy (due to motion) at the bottom.

The initial potential energy can be calculated using the formula:

Potential Energy = mass x acceleration due to gravity x height

where the mass is 17 kg, the acceleration due to gravity is 9.8 m/s² (approximately), and the height is 3.5 m.

Potential Energy = 17 kg x 9.8 m/s² x 3.5 m

Now, the kinetic energy at the bottom can be calculated as:

Kinetic Energy = (1/2) x mass x velocity²

We know the mass is 17 kg and the velocity is 4.5 m/s, so we can substitute these values into the equation:

Kinetic Energy = (1/2) x 17 kg x (4.5 m/s)²

According to the conservation of energy, the potential energy at the start is equal to the kinetic energy at the bottom:

Potential Energy = Kinetic Energy

Thus, we can set both equations equal to each other:

17 kg x 9.8 m/s² x 3.5 m = (1/2) x 17 kg x (4.5 m/s)²

Now, we can solve for the force of friction using the equation:

Force of Friction = Work / Distance

Here, the work done by friction is equal to the potential energy (since the total mechanical energy is conserved) and the distance is the height of the slide.

Substituting the values we found earlier, we get:

Force of Friction = (17 kg x 9.8 m/s² x 3.5 m) / 3.5 m

Simplifying the equation:

Force of Friction = 17 kg x 9.8 m/s²

Finally, we have the force of friction, which is equal to the work done by friction. So, the work done by friction as the child goes down the slide is:

Work = Force of Friction = 17 kg x 9.8 m/s²

Now you can calculate the numerical value of the work done by multiplying the mass (17 kg) by the acceleration due to gravity (9.8 m/s²).

PE = mg*h = 17*9.8*3.5 = 583.1 Joules.

KEo = 583.1 J. , No friction.

KE = 0.5m*V^2 = 8.5*4.5^2 = 172.1 J.,
With friction.

KE Lost = KEo-KE = 583.1-172.1 = 411 J.
= Work done by friction.