Kinetic friction - finding time

In summary, the conversation discusses a problem involving a skier on a slope with an initial velocity and a given coefficient of kinetic friction. The solution involves calculating the time taken for the skier to come to a stop using the formula delta t = (Vf - Vi) / a, where a is the acceleration calculated using the formula a = Fa / m. The conversation also clarifies the use of the kinetic friction formula and the necessary negative acceleration for the skier to slow down.
  • #1
inner08
49
0
Hi,

I'm not sure if I did this right but here is the word problem and the work I've done. If I made any errors, i'd love to know about them!

A sight seen on many bunny hills across Ontario is young skiers pushing on ski poles and gliding down a slope until they come to rest. Observing from a distance, you note a young person (approximately 25 kg) pushing off with the ski poles to give herself an initial velocity of 3.5 m/s. If the inclination of the hill is 5.0 degrees and the coefficient of kinetic friction for the skis on dry snow is 0.20, calculate

a) the time taken for the skier to come to a stop

For a:

Fa = Fgh + Ff
= Fg sin 5 (degrees) + ukFn


Fn = Fg cos 5 (degrees)
= mg cos 5 (degrees)

Fa = Fg sin 5(degrees) + ukmg cos 5 (degrees)
= mg sin 5(degrees) + ukmg cos 5(degrees)
= (25kg) (9.8m/s^2)(0.08716) + (0.20)(25kg)(9.8m/s^2)(0.9962)
= 70N

F = ma
a = 70N / 25kg
= 2.8 m/s^2


delta t = (Vf - Vi) / a
= (0 - 3.5m/s) / 2.8 m/s^2
= 1.25s

The time for the skier to come to a stop is 1.25 seconds.
 
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  • #2
inner08 said:
a) the time taken for the skier to come to a stop

For a:

Fa = Fgh + Ff
= Fg sin 5 (degrees) + ukFn
Realize that the kinetic friction opposes the skier's motion.
 
  • #3
Oh sorry..i'm still trying to get the hang of all of this. Its been a while since I did some physics.

So since the kinetic friction opposes the skier's motion, I would use the following formula: Fa = Fg sin 5 (degrees) - ukFn? Then I would just plug in the values like I did right?
 
  • #4
Yes. Realize that the acceleration--given your choice of sign convention--must be negative: opposite to the skier's direction of motion. Otherwise, the skier would speed up instead of slow down.
 

1. What is kinetic friction?

Kinetic friction is the force that opposes the motion of an object as it moves across a surface. It is caused by the contact between the object and the surface, and it depends on the materials and the roughness of the surfaces in contact.

2. How is kinetic friction different from static friction?

Kinetic friction occurs when an object is already in motion, while static friction occurs when an object is at rest and trying to be set in motion. Kinetic friction is typically weaker than static friction, as it takes more force to overcome static friction and start an object moving.

3. How can I calculate the time it takes for an object to stop due to kinetic friction?

To calculate the time it takes for an object to stop due to kinetic friction, you need to know the initial velocity of the object, the coefficient of kinetic friction between the object and the surface, and the mass of the object. You can then use the equation t = (m * v) / μk, where t is the time, m is the mass, v is the initial velocity, and μk is the coefficient of kinetic friction.

4. How does the surface affect the amount of kinetic friction?

The roughness of the surface has a significant impact on the amount of kinetic friction. Rougher surfaces create more friction, as there are more points of contact between the object and the surface. Smoother surfaces have less friction, making it easier for the object to slide or roll across them.

5. Can kinetic friction be reduced or eliminated?

Kinetic friction is a natural force that cannot be eliminated entirely. However, it can be reduced by using lubricants, such as oil or grease, between the object and the surface. These substances reduce the amount of friction between the two surfaces, allowing the object to move more easily. Additionally, using smoother surfaces or reducing the weight of the object can also help reduce the effects of kinetic friction.

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