A skier of mass 71.0 kg is pulled up a slope
by a motor-driven cable.
How much work is required to pull the skier
62.2 m up a 37.0� slope (assumed to be fric-
tionless) at a constant speed of 2.0 m/s? The
acceleration of gravity is 9.81 m/s2 .
To find the work required to pull the skier up the slope, we need to calculate the gravitational potential energy gained by the skier.
The gravitational potential energy is given by the formula:
Potential energy = mass * gravity * height
First, let's calculate the height the skier is being lifted using trigonometry. The 37.0 degree slope forms a right-angled triangle with the vertical height being the height the skier is being lifted (h) and the horizontal distance being the 62.2 meters.
Using trigonometry, the height (h) can be calculated as:
h = distance * sin(angle)
h = 62.2 m * sin(37.0°)
Now, let's calculate the gravitational potential energy gained by the skier:
Potential energy = mass * gravity * height
Potential energy = 71.0 kg * 9.81 m/s^2 * h
Finally, the work done to pull the skier up the slope is equal to the potential energy gained:
Work = Potential energy
Work = 71.0 kg * 9.81 m/s^2 * h
Using the values we get, you can calculate the work required to pull the skier up the slope.
Ws = mg = 71 kg * 9.81 N./kg = 696 N. =
Weight of skier.
Fs = 696 N. @ 37 Deg. = Force of skier.
Fp = 696*sin37 = 419 N. = Force parallel to slope.
Ff = 0 = Force of friction.
Fn = Fap - Fp - Ff = 0. a = o.
Fap-419-0 = 0,
Fap = 419 N. = Force applied.
h = 62.2*sin37 = 37.4 m.
W = Fap*h = 419 * 37.4 = 15,684 Joules