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
Ws = mg = 54.6 * 9.8 N./kg = 535.1 N. = Weight of skier.
Fs = 535.1 N. @ 21 Deg. = Force of skier.
Fp = 535.1*sin21 = Force parallel to the slope.
To find the force on the skier parallel to the slope, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
Step 1: Determine the component of the force of gravity parallel to the slope.
The force of gravity can be separated into two components: one parallel to the slope and one perpendicular to the slope. The component of the force of gravity parallel to the slope can be calculated using the following formula:
Force_parallel = m * g * sin(θ),
where:
m = mass of the skier (54.6 kg),
g = acceleration due to gravity (9.8 m/s²),
θ = angle of the slope (21°).
Step 2: Calculate the force on the skier parallel to the slope.
Plugging in the values, we have:
Force_parallel = 54.6 kg * 9.8 m/s² * sin(21°).
Calculating this expression, we find:
Force_parallel = 54.6 kg * 9.8 m/s² * sin(21°) ≈ 188.31 N.
Therefore, the force on the skier parallel to the slope is approximately 188.31 N.