A 67.5kg skier slides down a 20° slope whose vertical height is 125m. What is the variation of the potential energy of the skier?
well it gives you the height, not the length, so you do not need the 20 degrees
- m g h = -67.5 * 9.81 * 125 Joules of gravitational potential energy lost.
By the way
if there is no friction, that is (1/2) m v^2 the increase in kinetic energy.
Now if you need to calculate friction forces, you need to use the 20 degrees.
The potential energy of an object is given by the formula:
Potential Energy = mass * gravity * height
Given:
mass = 67.5 kg
gravity = 9.8 m/s^2
height = 125 m
Substituting these values into the formula:
Potential Energy = 67.5 kg * 9.8 m/s^2 * 125 m
Multiplying the values:
Potential Energy = 82687.5 kg*m^2/s^2
Simplifying:
Potential Energy = 82687.5 Joules
Therefore, the variation of potential energy of the skier is 82687.5 Joules.
To calculate the variation of potential energy of the skier, we first need to calculate the initial potential energy and the final potential energy.
The potential energy of an object is given by the equation:
Potential Energy = mass * gravity * height
where:
- mass is the mass of the object (in kilograms)
- gravity is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
- height is the vertical height of the object (in meters)
Given:
- mass = 67.5 kg
- height = 125 m
Let's calculate the initial potential energy when the skier is at the top of the slope:
Potential Energy (initial) = mass * gravity * height
= 67.5 kg * 9.8 m/s^2 * 125 m
Now, to calculate the final potential energy when the skier is at the bottom of the slope, we need to use the vertical height along the slope.
The vertical height along the slope can be calculated as follows:
Vertical Height = height * sin(angle)
where:
- angle is the angle of the slope (in degrees)
Given:
- angle = 20°
Let's calculate the vertical height along the slope:
Vertical Height = 125 m * sin(20°)
Now, we can calculate the final potential energy when the skier is at the bottom of the slope:
Potential Energy (final) = mass * gravity * Vertical Height
Finally, we can calculate the variation in potential energy:
Variation of Potential Energy = Potential Energy (final) - Potential Energy (initial)
I'll calculate the values for you.