A skier of mass 65.0 kg is pulled up a slope by a motor-driven cable. How much work is required to pull the skier 57.0 m up a 35° slope (assumed to be frictionless) at a constant speed of 2.0 m/s?
J
The vertical rise is
H = 57 sin 35 meters.
The work required to raise the skier that amount is M g H.
It does not depend upon the speed, although the required power does.
To find the work required to pull the skier up the slope, we can use the formula:
Work = Force * Distance * cos(theta)
where:
- Force is the force applied to pull the skier up the slope
- Distance is the distance traveled up the slope
- theta is the angle between the force and the direction of motion (35° in this case)
First, let's calculate the force required to pull the skier up the slope. We can use the equation:
Force = Mass * Acceleration
Since the skier is moving at a constant speed, the acceleration is zero. Therefore, the force required to counteract the gravitational force acting on the skier can be calculated as:
Force = Mass * (gravitational acceleration * sin(theta))
where:
- Mass is the mass of the skier (65.0 kg)
- Gravitational acceleration is the acceleration due to gravity (approximately 9.8 m/s^2)
- theta is the angle of the slope (35°)
Force = 65.0 kg * (9.8 m/s^2 * sin(35°))
Now, we can calculate the work by multiplying the force by the distance and by the cosine of theta:
Work = Force * Distance * cos(theta)
Work = (65.0 kg * (9.8 m/s^2 * sin(35°))) * 57.0 m * cos(35°)
Finally, substitute the values into the equation and solve for the work:
Work = (65.0 kg * (9.8 m/s^2 * sin(35°))) * 57.0 m * cos(35°)
After performing the calculations, you will find the work required to pull the skier up the slope.