How to Find Distance in Physics Knowing Static Friction
A wheel rolling over a surface overcomes static friction. If it could not, the wheel would stop rolling. Static friction depends on many things such as the wheel material, axle friction and the surface rolled upon. It does not depend on the mass of the vehicle, however. The combination of a few rules of physics will allow you to calculate the distance an object, such as how far a car will roll before coming to a stop.
Other People Are Reading
Instructions
-
-
1
Calculate the distance the object will travel at an initial velocity (v) until it stops, when velocity is zero. The initial kinetic energy of the object equals 1/2 times the mass times v squared (1/2*m*v^2). The final kinetic energy of the object equals zero.
-
2
Define work as the change in the kinetic energy of an object. The object goes from a kinetic energy of 1/2*m*v^2 to zero, so the change in kinetic energy equals -1/2*m*v^2.
-
-
3
Define the force of friction: the coefficient of friction (mu, written as u) times mass times the acceleration due to gravity (g). Because it operates against the velocity of the object, it is negative; in shorthand -u*m*g. Because the object is rolling to a stop, u is static friction.
-
4
Define work as force times distance (d). In this case, the force is the force of friction. Substituting the formula from Step 3, the force times the distance equals -u*m*g*d.
-
5
Check the values work you calculated in Step 2 and Step 4. They will be identical.
Work = -1/2*m*v^2 = -u*m*g*d
You can reduce this equation by multiplying both sides by -m.
-1/2*m*v^2 = -u*m*g*d
1/2*v^2 = u*g*d
-
6
Isolate d in the equation to find the distance the object rolls.
1/2*v^2 = u*g*d
d=(v^2)/2*u*g
The acceleration due to gravity is a constant: 9.8 m/s^2 in metric units and 32.2 ft/s^2 in imperial units.
To calculate distance rolled to a stop, you need know only static friction (u) and the initial velocity (v).
-
1
