Finding stopping distance given coefficient of kinetic friction and mass

[disque]

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

 

[tiny-tim]

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!

(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.

 

[nlightner]

.

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.