A 60 kg skier is coming down a hill that has an incline of 35°.
If the force of friction between the ski and the snow is 6 N, how fast does the velocity change per second?
the gravitational force parallel to the slope is ... m g sin(35º)
find the net force ... gravity - friction
acceleration = net force / mass
To determine how fast the velocity changes per second, we need to calculate the net force acting on the skier along the direction of motion. This can be done by subtracting the force of friction from the component of the gravitational force that acts along the incline.
First, let's calculate the component of the gravitational force parallel to the incline. This can be determined by multiplying the gravitational force (weight) of the skier by the sine of the angle of the incline.
Weight of the skier = mass x acceleration due to gravity
Weight = 60 kg x 9.8 m/s^2 (approximating acceleration due to gravity)
Next, we can calculate the force parallel to the incline.
Force parallel to the incline = Weight x sin(theta)
Force parallel to the incline = (60 kg x 9.8 m/s^2) x sin(35°)
Now, to find the net force along the direction of motion, we subtract the force of friction from the force parallel to the incline.
Net force along the direction of motion = Force parallel to the incline - Force of friction
Net force = (60 kg x 9.8 m/s^2 x sin(35°)) - 6 N
Finally, we can obtain the acceleration by dividing the net force by the mass of the skier.
Acceleration = Net force / mass
Acceleration = [(60 kg x 9.8 m/s^2 x sin(35°)) - 6 N] / 60 kg
Once we have the acceleration, we can calculate how fast the velocity changes per second. The rate of change of velocity is equal to the acceleration.
Therefore, the velocity changes at a rate equal to the calculated acceleration.