A 37 kg child roller skates, initially at rest, rolls 2.0 m down an incline at an angle of 17 degrees with the horizontal. If there's no friction, what is the kinetic energy of the child at the bottom of the incline?
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To find the kinetic energy of the child at the bottom of the incline, we need to know the formula for kinetic energy and the velocity of the child at that point.
The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity^2
First, let's calculate the velocity of the child at the bottom of the incline.
To do that, we'll use the principles of conservation of energy. At the top of the incline, the child only has potential energy (due to the height) which converts completely into kinetic energy at the bottom (as there is no friction).
The potential energy at the top of the incline can be calculated using:
Potential Energy = mass * gravity * height
where the mass is 37 kg, gravity is 9.8 m/s^2, and the height can be found using:
height = distance * sin(angle)
where the distance is 2.0 m and the angle is 17 degrees.
Let's calculate the potential energy:
height = 2.0 m * sin(17 degrees) = 0.567 m
Potential Energy = 37 kg * 9.8 m/s^2 * 0.567 m = 200.6952 J (rounded to 4 decimal places)
Since there is no energy loss, this potential energy will be converted to kinetic energy at the bottom. Therefore, the kinetic energy at the bottom is equal to the potential energy at the top:
Kinetic Energy = 200.6952 J
So, the kinetic energy of the child at the bottom of the incline is approximately 200.6952 Joules.