A skier of mass 75.0 kg is pulled up a slope by a motor-driven cable. How much work is required to pull the skier 60.0 m up a 35° slope (assumed to be frictionless) at a constant speed of 2.0 m/s?
To calculate the work required to pull the skier up the slope, we can use the formula:
Work = Force x Distance x cos(theta)
Where:
- Work is the amount of work done (measured in joules, J)
- Force is the force applied to pull the skier (measured in newtons, N)
- Distance is the distance the skier is pulled up the slope (measured in meters, m)
- theta is the angle of the slope relative to the horizontal (35° in this case)
First, we need to calculate the force required to pull the skier up the slope. This can be done using Newton's second law of motion:
Force = mass x acceleration
Since the skier is moving at a constant speed of 2.0 m/s, there is no acceleration. Therefore, the force required to counteract the force of gravity (which pulls the skier downwards) can be calculated using the equation:
Force = mass x gravity
Where:
- mass is the mass of the skier (measured in kilograms, kg)
- gravity is the acceleration due to gravity (approximately 9.8 m/s^2)
Substituting the given values into the equation, we have:
Force = 75.0 kg x 9.8 m/s^2 = 735.0 N
Next, we can calculate the work done by substituting the values into the work formula:
Work = 735.0 N x 60.0 m x cos(35°)
Note that we need to convert the angle from degrees to radians before calculating the cosine function. To do this, we use the formula:
radians = degrees x (π/180)
So, the angle in radians is:
35° x (π/180) = 35π/180 radians
Substituting the values into the work formula, we have:
Work = 735.0 N x 60.0 m x cos(35π/180)
Now, you can calculate the work required to pull the skier up the slope by evaluating the expression.