a bar is pushed so that it slides across the floor. how far will it go, given the coefficient of kinetic friction is 0.25, and the push imparts an initial speed of 2.5m/s?
stopping force = -.25 * m * 9.8
F = m a
a = -.25 * 9.8 = -2.45 m/s^2
v = 2.5 - 2.45 t
so stops at t = 1.02 seconds
x = 2.5 * 1.02 + (1/2)(-2.45) (1.02)^2
x = 2.55 - 1.27 = 1.28 m
To solve this problem, we can use the concept of work and energy. The work done on an object is equal to the change in its kinetic energy.
1. Calculate the initial kinetic energy (KE) of the bar using the formula:
KE = (1/2) * mass * (initial velocity)^2
2. Determine the work done against friction by multiplying the initial kinetic energy by the coefficient of kinetic friction:
Work = KE * coefficient of kinetic friction
3. The work done against friction is also equal to the change in kinetic energy. Since the final kinetic energy will be zero (the bar stops), we have:
Work = (1/2) * mass * (final velocity)^2
4. Rearrange the equation to solve for the final velocity:
(final velocity)^2 = 2 * Work / mass
5. Substitute the known values into the equation and solve for the final velocity:
(final velocity)^2 = (2 * Work) / mass
6. Take the square root of both sides of the equation to find the final velocity:
final velocity = sqrt((2 * Work) / mass)
Once you have the final velocity, you can determine how far the bar will go using the equation for displacement:
Displacement = (initial velocity * time) - (1/2) * (coefficient of kinetic friction) * (time^2)
Substitute the initial velocity and the known coefficient of kinetic friction into the equation to calculate the displacement.