A 69 kg person on skis is going down a hill sloped at 36° below the horizontal (+x direction). The coefficient of friction between the skis and the snow is 0.15. Find the x and y components of the weight of the skier going downhill.
Ws = mg = 69 kg * 9.8 N/kg = 676.2 N. =
Weigth of skier.
Fs = 676.2 N. @ 36 deg.=Force of skier.
Fp = X = 676.2*sin36 = 397.5 N. = Force parallel to hill.
Fv = Y = 676.2*cos36 = 547.1 N. = Force
perpendicular to hill.
To find the x and y components of the weight of the skier going downhill, we can start by calculating the total weight of the skier.
First, we need to find the gravitational force acting on the skier. We can use the formula:
Weight = mass * gravitational acceleration
Given that the mass of the skier is 69 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the weight:
Weight = 69 kg * 9.8 m/s^2 = 676.2 N
Now, let's find the x and y components of the weight.
The weight can be resolved into two components:
Horizontal component (x direction): Weight_x = Weight * sin(θ)
Vertical component (y direction): Weight_y = Weight * cos(θ)
where θ is the angle of the slope, which is 36° below the horizontal.
Now, let's calculate the x and y components:
Weight_x = 676.2 N * sin(36°) ≈ 676.2 N * 0.5878 ≈ 397.76 N
Weight_y = 676.2 N * cos(36°) ≈ 676.2 N * 0.8090 ≈ 546.88 N
Therefore, the x component of the weight of the skier going downhill is approximately 397.76 N, and the y component is approximately 546.88 N.
To find the x and y components of the weight of the skier going downhill, we need to break down the weight vector into its x and y components.
Step 1: Calculate the weight of the skier.
The weight of an object is given by the equation W = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the skier is 69 kg, we can calculate the weight as:
W = 69 kg * 9.8 m/s^2 = 676.2 N
Step 2: Calculate the x and y components of the weight.
The x and y components of the weight vector can be found using trigonometry. Remember that the angle is measured below the horizontal, so in this case, the x component will be negative.
To find the x component:
Wx = W * sin(θ)
Wx = 676.2 N * sin(36°)
Wx ≈ - 405 N
To find the y component:
Wy = W * cos(θ)
Wy = 676.2 N * cos(36°)
Wy ≈ 546 N
Therefore, the x component of the weight of the skier going downhill is approximately -405 N (negative because it acts in the opposite direction of the positive x-axis), and the y component is approximately 546 N.