How to Calculate Distance Traveled on a Slope with Kinetic Friction

In summary, two skiers discuss the distance an Olympic skier will travel down a 24 degree slope at a speed of 28 m/s before coming to a halt on a region of snowless ground with a coefficient of kinetic friction of 0.67. They come up with an equation to solve for the distance traveled and the acceleration, with the final solution being approximately 195.25 meters.
  • #1
hoseA
61
0
An Olympic skier moving at 28 m/s down
a 24 degrees slope encounters a region of snowless
ground of coefficient of kinetic friction 0.67.
The acceleration of gravity is 9.8 m/s^2
How far down the slope does she travel
before coming to a halt? Answer in units of
m.

I came up with an equation of:

mgsin(theta) - Fk*d = ma

I would solve for "d" but I'm not sure how to get the "a".

help appreciated.

TIA.
 
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  • #2
Try this,

The sum of the forces parallel to the slope is mgcos62(gravity) - mgUk(friction)

mg(Uk-cos62) = - 0.21 mg = -2.06m/s^2 * m

so your acceleration, a, is 2.06 m/s^2 going against the skier.

From there you use t = dv/a = 28/2.06 so t = 13.6 s

then L traveled is L = 1/2 a t^2 = 44.8 m

Or something like that.
 
  • #3
civil_dude said:
Try this,
The sum of the forces parallel to the slope is mgcos62(gravity) - mgUk(friction)
mg(Uk-cos62) = - 0.21 mg = -2.06m/s^2 * m
so your acceleration, a, is 2.06 m/s^2 going against the skier.
From there you use t = dv/a = 28/2.06 so t = 13.6 s
then L traveled is L = 1/2 a t^2 = 44.8 m
Or something like that.

Thanks a lot. Your math is off in the last step but you had the right concepts.

I did mgsin(theta)-Ukmgcos(theta) = ma

a = 2.01...

t = 28/2.01...

L = .5at^2 = 195.25 (not precise but within 1% margin of error)

Thanks again. :)
 

What is kinetic friction?

Kinetic friction is the force that opposes the motion of two surfaces that are in contact with each other. It is caused by microscopic irregularities on the surfaces that create resistance when they come into contact.

How is kinetic friction different from static friction?

Kinetic friction occurs when two surfaces are already in motion, while static friction occurs when two surfaces are at rest and prevent motion from occurring. Kinetic friction is typically lower than static friction.

What factors affect the magnitude of kinetic friction?

The magnitude of kinetic friction is affected by the types of materials in contact, the roughness of the surfaces, the normal force, and the velocity of the moving object.

How is the coefficient of kinetic friction calculated?

The coefficient of kinetic friction is calculated by dividing the force of kinetic friction by the normal force. It is a dimensionless quantity and varies based on the materials in contact.

How can kinetic friction be reduced?

Kinetic friction can be reduced by using lubricants, such as oil or grease, to create a smoother surface between the two objects in contact. Additionally, using materials with lower coefficients of friction can also reduce kinetic friction.

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