A skier of mass 70.5 kg is pulled up a slope by a motor-driven cable. How much work is required to pull the skier 60 m up a 38° slope (assumed to be frictionless) at a constant speed of 2.0 m/s?
The elevation gain is
H = 60 sin38 = 36.9 m
The energy required is the potential energy gain,
E = M g H
The speed does not matter, as long as it is constant. Kinetic energy stays the same.
25521 J
work=20,580J
power=686 watts
18081 J
A skier of mass 61.0 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 40.0 m up a 30.0° slope (assumed frictionless) at a constant speed of 4.00 m/s? (b) What power must a motor have to perform this task?
skier of mass 79 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him 80 m up a 30° slope (assumed frictionless) at a constant speed of 3.4 m/s?
1 J
(b) What power (expressed in hp) must a motor have to perform this task?
To find the work required to pull the skier up the slope, we need to find the force needed to move the skier at a constant speed and the distance covered.
First, we need to find the force required to pull the skier up the slope. The force can be calculated using the equation:
Force = Mass * Acceleration
Since the skier is moving at a constant speed, the acceleration is zero.
Force = Mass * Acceleration = 70.5 kg * 0 m/s^2 = 0 N
Next, we need to find the component of the gravitational force acting down the slope, which is responsible for pulling the skier down. The gravitational force can be calculated using:
Gravitational Force = Mass * Gravity
where gravity is the acceleration due to gravity, approximately 9.8 m/s^2.
Gravitational Force = 70.5 kg * 9.8 m/s^2 = 690.9 N
The component of the gravitational force acting down the slope can be found using:
Force_down_slope = Gravitational Force * sin(θ)
where θ is the angle of the slope. In this case, θ = 38°.
Force_down_slope = 690.9 N * sin(38°) = 423.8 N
Since the skier is moving at a constant speed, the force required to pull the skier up the slope must be equal in magnitude but opposite in direction to the force down the slope.
Therefore, the force required to pull the skier up the slope is 423.8 N.
Now, we can calculate the work done using the equation:
Work = Force * Distance * Cosine(θ)
where the distance is 60 m and θ is the angle of the slope, which is 38°.
Work = 423.8 N * 60 m * Cosine(38°)
Calculating this value gives us the amount of work required to pull the skier up the slope.
Note: The Cosine function is used instead of the Sine function, as we are interested in the work done in the direction of the motion (along the slope) and not the perpendicular direction.
After performing the necessary calculations, the work required to pull the skier up the slope is approximately 24,423.6 Joules (J).