The kinetic friction force between a 60kg object and a horizontal surface is 50N. If the initial speed of the object is 25m/s, what distance will it slide before coming to a stop?
To find the distance the object will slide before coming to a stop, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the object comes to a stop)
u = initial velocity (25 m/s)
a = acceleration (due to the kinetic friction force)
s = distance
First, let's find the acceleration:
The friction force can be calculated using the equation:
friction force = µ * normal force
Where:
µ = coefficient of kinetic friction (unknown)
normal force = mass * acceleration due to gravity (mg)
Given that the friction force is 50N, and the mass is 60kg, we can calculate the normal force:
normal force = mass * acceleration due to gravity
= 60kg * 9.8 m/s^2
= 588N
Using the equation for friction force, we can find the coefficient of kinetic friction:
50N = µ * 588N
Simplifying the equation, we get:
µ = 50N / 588N
≈ 0.085
Now that we have the coefficient of kinetic friction, we can substitute this value along with the initial velocity (u = 25 m/s) into the equation of motion:
0 = (25 m/s)^2 + 2 * µ * 9.8 m/s^2 * s
Simplifying the equation, we get:
0 = 625 m^2/s^2 + 19.6 m/s^2 * s
Rearranging the equation, we get:
19.6 m/s^2 * s = -625 m^2/s^2
Dividing both sides by 19.6 m/s^2, we get:
s = -625 m^2/s^2 / 19.6 m/s^2
= -32 m^2/s^2
Since the distance cannot be negative, we take the absolute value:
s = 32 m^2/s^2
Therefore, the object will slide approximately 32 meters before coming to a stop.