A 65.0-kg skier coasts up a snow-covered hill that makes an angle of 27.4° with the horizontal. The initial speed of the skier is 6.37 m/s. After coasting 2.07 m up the slope, the skier has a speed of 4.06 m/s. Calculate the work done by the kinetic frictional force that acts on the skis.
can someone explain this question to me please?
Certainly! This question involves calculating the work done by the kinetic frictional force acting on a skier.
To solve this problem, you need to understand the concept of work and the relationship between work and friction. Work is defined as the product of the force applied on an object and the displacement of the object in the direction of the force.
In this case, the force we are interested in is the kinetic frictional force acting on the skis, which opposes the skier's motion up the slope. The displacement referred to in the problem is the distance traveled up the slope by the skier.
To calculate the work done by the kinetic frictional force, we can follow these steps:
1. Break the force into its components:
- The force of gravity acting vertically downwards.
- The component of the force of gravity acting parallel to the slope, which is responsible for pulling the skier downwards.
- The component of the force of gravity acting perpendicular to the slope, which is responsible for pushing the skier into the slope.
2. Calculate the component of the force of gravity pulling the skier downwards:
- This can be done using trigonometry and the angle of the slope. The formula is:
Force_downward = Mass * Acceleration_due_to_gravity * sin(slope angle)
3. Determine the net force acting on the skier in the direction of motion:
- This is the difference between the force dragging the skier down the slope and the force pushing the skier into the slope.
- Net_force = Force_downward - Force_perpendicular
4. Calculate the work done by the kinetic frictional force:
- The formula for work is: Work = Force_parallel * Distance
- In this case, the distance is given as 2.07 m.
Therefore, by plugging in the given values and following these steps, you can find the work done by the kinetic frictional force acting on the skis.
height gained = h = 2.07 sin 27.4
Potential energy gained = m g h
Ke lost = (1/2)m (6.37^2 - 4.06^2)
work done by friction = difference