A 71-kg skier is going down a slope oriented 37° above the horizontal. The area of each ski in contact with the snow is 0.13 m2. Determine the pressure that each ski exerts on the snow.
To determine the pressure that each ski exerts on the snow, you can use the following formula:
Pressure (P) = Force (F) / Area (A)
First, let's calculate the force exerted by each ski on the snow.
To find the force, we'll use the formula:
Force (F) = Mass (m) × Acceleration (a)
Given that the skier's mass is 71 kg, we can use the equation:
Force (F) = 71 kg × Acceleration
Now, to find the acceleration, we'll use the equation:
Acceleration (a) = gravitational acceleration (g) × sin(θ)
Given that the slope is oriented 37 degrees above the horizontal, we can determine the angle (θ):
θ = 37°
The gravitational acceleration (g) is a standard constant:
g = 9.8 m/s^2
So, the acceleration (a) is:
a = 9.8 m/s^2 × sin(37°)
Now that we have the acceleration, we can calculate the force (F) exerted:
F = 71 kg × (9.8 m/s^2 × sin(37°))
Next, we need to determine the area (A) of each ski in contact with the snow. The area given is 0.13 m^2.
Now, we have both the force (F) and the area (A), so we can calculate the pressure (P):
P = F / A = (71 kg × (9.8 m/s^2 × sin(37°))) / 0.13 m^2
Calculating this expression will give you the pressure exerted by each ski on the snow.