A 60-kg person on skis is going down a hill sloped at 30° from the horizontal. The coefficient of friction between the skis and the snow is 0.17. What would be the magnitude of the acceleration?
Plz help
To find the magnitude of acceleration, we need to consider the forces acting on the person on skis.
First, let's consider the gravitational force. The weight of the person can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 60 kg × 9.8 m/s²
Weight = 588 N
Next, we need to consider the frictional force opposing the motion. The formula for frictional force is:
Frictional force = coefficient of friction × normal force
To calculate the normal force, we need to break down the weight force into its components. The normal force will act perpendicular to the incline and cancel out the component of the weight force acting parallel to the incline.
Normal force = weight × cosine(angle)
Normal force = 588 N × cos(30°)
Normal force = 588 N × √3/2
Normal force = 588 N × 0.866
Normal force = 509.808 N
Now, we can calculate the frictional force:
Frictional force = 0.17 × 509.808 N
Frictional force = 86.564 N
Since the person is moving downhill, the frictional force will act in the opposite direction of motion. Therefore, we can subtract it from the weight force to calculate the net force acting on the person:
Net force = weight - frictional force
Net force = 588 N - 86.564 N
Net force = 501.436 N
Finally, we can calculate the magnitude of acceleration using Newton's second law:
Net force = mass × acceleration
501.436 N = 60 kg × acceleration
acceleration = 501.436 N / 60 kg
acceleration ≈ 8.356 m/s²
Therefore, the magnitude of the acceleration of the person on skis is approximately 8.356 m/s².