A skier is traveling down the slopes of one of the greatest artificially created mountains in all of Brampton….Mt. Brampton. The initial speed of the skier is 21. m/s. The skier has a mass of 75. kg. The coefficient of kinetic friction is 0.20 and the force due to air resistance is 42. N.
What is the acceleration? Show your work.
To find the acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The skier experiences two forces that oppose its motion: the force due to friction and the force due to air resistance. The force due to friction can be calculated using the equation:
Force of friction = coefficient of friction * normal force
The normal force is equal to the weight of the skier, which is calculated as:
Weight = mass * gravity
where gravity is approximately 9.8 m/s².
So, the force of friction can be calculated as:
Force of friction = 0.20 * (mass * gravity)
Next, we subtract the force due to air resistance from the force of friction to obtain the net force acting on the skier:
Net force = Force of friction - Force due to air resistance
Finally, we use Newton's second law to find the acceleration:
Net force = mass * acceleration
Rearranging the equation, we can solve for acceleration as:
Acceleration = Net force / mass
Now let's calculate the values step by step:
1. Weight (force due to gravity):
Weight = mass * gravity
Weight = 75 kg * 9.8 m/s²
2. Force of friction:
Force of friction = coefficient of friction * normal force
Force of friction = 0.20 * Weight (from step 1)
3. Net force:
Net force = Force of friction - Force due to air resistance
Net force = Force of friction - 42 N
4. Acceleration:
Acceleration = Net force / mass
By following these steps and substituting the values, you can find the acceleration of the skier.