A skier of mass 54.6 kg comes down a slope of constant angle 21◦ with the horizontal.
The acceleration of gravity is 9.8 m/s2 .
What is the force on the skier parallel to the slope?
Answer in units of N
To find the force on the skier parallel to the slope, you can use the formula for the force component in the direction of the slope:
Force_parallel = mass * acceleration_due_to_gravity * sin(angle)
Given:
Mass (m) = 54.6 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Angle (θ) = 21°
First, convert the angle from degrees to radians:
angle_radians = angle * (π/180)
angle_radians = 21° * (π/180) ≈ 0.36651 radians
Next, plug in the values into the formula:
Force_parallel = 54.6 kg * 9.8 m/s^2 * sin(0.36651 radians)
Using a scientific calculator, evaluate the sine value:
sin(0.36651 radians) ≈ 0.35836
Now, calculate the force:
Force_parallel ≈ 54.6 kg * 9.8 m/s^2 * 0.35836
Solving the equation gives us:
Force_parallel ≈ 191.24 N
Therefore, the force on the skier parallel to the slope is approximately 191.24 N.