Skier on a slope with friction (looking for final velocity)

In summary, the question asks for the speed of a 75kg skier starting down a 50m high 10˚ slope, assuming frictionless skis in Part A and a coefficient of kinetic friction of µk=.05 in Part B. After calculating the length of the slope to be 288m and the initial velocity to be 0m/s, the final velocity for Part A is determined to be 31m/s. In Part B, the normal force (FN) is calculated to be 724.6N using Newton's second law and the friction force (Ff) is found to be the product of the normal force and the coefficient of kinetic friction. The acceleration of the skier can then be calculated
  • #1
Cmertin
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0

Homework Statement


A 75Kg skier starts down a 50m high 10˚ slope. What is his speed at the bottom?
Part A: Consider skis frictionless
Part B: Assume that the coefficient of kinetic friction between the skis and the surface of the slope is µk=.05

Homework Equations


|Ff|=µk•|FN|
Fnet=-Ff+FN+Fg=0=ma
a=g•sin(ø) (pretend that chi is theta)
FN=ma•cos(ø)

Values I figured out from Part A:
The length of the slope (on the hypotenuse) is 288m
Initial velocity in both the X and Y is 0m/s
For part A, the final velocity is 31m/s (does not need to be checked)

The Attempt at a Solution


Part A:
I got part A with 31 m/s and I know it's right.

Part B:
0=Fnet=Fg+FN-Ff=ma (Newton's second law)
Ff=Fg+FN
FN=75Kg•9.81m/s2•cos(10˚)=724.6N
I think that I have to plug the normal force into the friction equation (|Ff|=µk•|FN|
) though I'm not sure if I have to and then I don't know what I would do after that.
 
Last edited:
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  • #2
Cmertin said:
Part B:
0=Fnet=Fg+FN-Ff=ma (Newton's second law)
Ff=Fg+FN
FN=75Kg•9.81m/s2•cos(10˚)=724.6N
I think that I have to plug the normal force into the friction equation (|Ff|=µk•|FN|
) though I'm not sure if I have to and then I don't know what I would do after that.
Yeah, the friction force is the result of the normal force and the coeff. of kinetic friction product. Once knowing the friction force, you already have the two forces acting in the slope, don't you? One is the Fx (that should be a component of Fg) and the other one is the friction itself. Then you can work out the acceleration.

Edit: I don't see how do you say that Fnet = 0. If that was the case in the x axis, there would be no acceleration. Moreover, you state 'Ff=Fg+FN' how do you find it to be so? Again, friction force is the normal (or Fy) times the coeff. of kinetic friction. Drawing the FBD is really helpful.
 
Last edited:

Related to Skier on a slope with friction (looking for final velocity)

1. What is the equation for calculating the final velocity of a skier on a slope with friction?

The equation for calculating the final velocity of a skier on a slope with friction is vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

2. How do I determine the acceleration of a skier on a slope with friction?

The acceleration of a skier on a slope with friction can be determined using the formula a = μg cos(θ), where μ is the coefficient of friction, g is the acceleration due to gravity (9.8 m/s2), and θ is the angle of the slope.

3. Can the final velocity of a skier on a slope with friction be negative?

Yes, the final velocity of a skier on a slope with friction can be negative if the skier is moving in the opposite direction of the initial velocity. This means that the skier is slowing down and has a negative acceleration.

4. How does the mass of the skier affect the final velocity on a slope with friction?

The mass of the skier does not directly affect the final velocity on a slope with friction. However, a heavier skier may experience more friction and therefore have a lower final velocity compared to a lighter skier on the same slope.

5. What is the role of air resistance in calculating the final velocity of a skier on a slope with friction?

Air resistance does not play a significant role in calculating the final velocity of a skier on a slope with friction, unless the slope is very steep. In most cases, the effect of air resistance can be ignored and the equations for motion with friction can be used to calculate the final velocity.

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