Finding stopping distance given coefficient of kinetic friction and mass

In summary, the problem is about finding the distance at which a bobsled, with a mass of 210 kg and starting from rest at point A, will come to a halt on a hill with negligible friction between points A and D and a coefficient of kinetic friction of 0.4 between points D and E. The approach involves calculating the work done by friction and using the work-energy theorem to find the distance.
  • #1
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Homework Statement


Bobsled

A bobsled run leads down a hill as sketched in the figure above. Between points A and D, friction is negligible. Between points D and E at the end of the run, the coefficient of kinetic friction is µk = 0.4. The mass of the bobsled with drivers is 210 kg and it starts from rest at point A.

Find the distance x beyond point D at which the bobsled will come to a halt.


Homework Equations


PE=mgy
(delta)x = ½ v_o2/ mg


The Attempt at a Solution


I thought the bottom equation should be the right approach but I don't know how to find the velocity given the coefficient of kinetic friction and mass of the sled
 

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  • #2
disque said:
A bobsled run leads down a hill as sketched in the figure above. Between points A and D, friction is negligible. Between points D and E at the end of the run, the coefficient of kinetic friction is µk = 0.4. The mass of the bobsled with drivers is 210 kg and it starts from rest at point A.

Find the distance x beyond point D at which the bobsled will come to a halt.

Hi disque! :smile:

(I can't see the picture yet)

This is an energy question …

calculate the the work done by friction,

and use the work-energy theorem, which says that loss of energy equals work done. :wink:
 
  • #3
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I would suggest using the equations of motion to solve this problem. The bobsled's motion can be described by the following equations:

1. v = u + at (velocity as a function of initial velocity, acceleration, and time)
2. x = ut + ½at^2 (distance as a function of initial velocity, acceleration, and time)
3. v^2 = u^2 + 2ax (velocity squared as a function of initial velocity, acceleration, and distance)

In this case, we know that the bobsled starts from rest (u = 0) and that the only force acting on it is the force of friction (F = µk * mg). We can use the first equation to solve for the time it takes for the bobsled to come to a halt:

v = 0 (since the sled comes to a halt)
u = 0 (since the sled starts from rest)
a = F/m = µk * g
t = v/a = 0/(µk * g) = 0 (since the sled starts from rest)

Therefore, the time it takes for the bobsled to come to a halt is 0 seconds. Now, we can use the second equation to solve for the distance x beyond point D:

x = ut + ½at^2 = 0 + ½(µk * g)(0)^2 = 0

This means that the bobsled will come to a halt at point D and will not travel any further.

To verify this result, we can also use the third equation to calculate the velocity at point D:

v^2 = u^2 + 2ax = 0^2 + 2(µk * g)(0) = 0

This confirms that the bobsled will have a velocity of 0 at point D and will not travel any further.

In conclusion, given the coefficient of kinetic friction and mass of the bobsled, we can calculate that the bobsled will come to a halt at point D and will not travel any further. This is due to the fact that there is no initial velocity and the frictional force acting on the sled will bring it to a stop in a very short amount of time.
 

What is stopping distance?

Stopping distance refers to the distance traveled by an object from the moment its brakes are applied until it comes to a complete stop.

What is coefficient of kinetic friction?

Coefficient of kinetic friction is a measure of the frictional force between two surfaces in contact when one of the surfaces is in motion.

How do you calculate stopping distance?

Stopping distance can be calculated using the formula: Stopping Distance = (Initial Velocity)^2 / (2 * Coefficient of Kinetic Friction * Acceleration Due to Gravity).

What is the role of mass in finding stopping distance?

The mass of an object affects its inertia, or resistance to changes in motion. Therefore, the greater the mass, the greater the stopping distance will be.

What are some factors that can affect stopping distance?

Factors that can affect stopping distance include the coefficient of kinetic friction, mass of the object, initial velocity, and acceleration due to gravity. Other factors such as road conditions, weather, and type of brakes can also play a role in determining stopping distance.

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