197k views
2 votes
A 16. 0 kg child on roller skates, initially at rest, rolls 2. 0 m down an incline at an angle of 20. 0° with the horizontal. If there is no friction between incline and skates, what is the kinetic energy of the child at the bottom of the incline?

1 Answer

3 votes

Okay, let's solve this step-by-step:

* We are given the mass of the child is 16.0 kg

* The child rolls 2.0 meters down an incline at an angle of 20.0 degrees

* We are told there is no friction, so all the potential energy will be converted to kinetic energy

* Since the child starts at rest, the initial kinetic energy is 0

* The formula for potential energy is: PE = mgh

- Where m is mass, g is acceleration due to gravity (9.8 m/s^2), and h is height

* Since the angle of the incline is 20.0 degrees, we can find the vertical height using trigonometry:

- h = 2.0m * sin(20.0 degrees)

- h = 0.347m

* Now we can find the initial potential energy:

- PE = (16.0kg)*(9.8m/s^2)*(0.347m)

- PE = 56.4 J

* Since all the potential energy is converted to kinetic energy, the final kinetic energy will be 56.4 J.

So the answer is: The kinetic energy of the child at the bottom of the incline is 56.4 Joules.

User Artem  Demchenko
by
8.6k points