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?
To find the kinetic energy of the child at the bottom of the incline, we can use the equation for kinetic energy:
Kinetic energy (KE) = 1/2 * mass * velocity^2
First, let's find the velocity of the child at the bottom of the incline using energy conservation. At the top of the incline, the child has only potential energy, and at the bottom, they have both potential energy and kinetic energy.
The potential energy (PE) at the top of the incline is given by:
PE = mass * g * height
where g is the acceleration due to gravity (approximately 9.8 m/s^2) and height is the vertical distance the child has traveled down the incline. The height can be found using the angle and the horizontal distance traveled:
height = distance * sin(angle)
In this case, the distance is given as 2.0 m, and the angle is 17 degrees.
Now, we can find the potential energy at the top of the incline:
PE = 37 kg * 9.8 m/s^2 * 2.0 m * sin(17 degrees)
Next, we need to find the velocity at the bottom of the incline. If there is no friction, all the potential energy is converted to kinetic energy. So, the potential energy at the top equals the kinetic energy at the bottom.
KE = PE
Finally, we can substitute the known values into the equation to find the kinetic energy:
KE = 37 kg * 9.8 m/s^2 * 2.0 m * sin(17 degrees)
Using a calculator, you can find the result to get the kinetic energy of the child at the bottom of the incline.
M g H
where H is the change in vertical elevation.
Get H from the length and the angle/