Suppose that the coefficient of friction between your feet and the floor, while wearing socks, is 0.250. Knowing this, you decide to get a running start and then slide across the floor. If your speed is 3.00 m/s when you start to slide, what distance, d, will you slide before stopping?
(initial kinetic energy) = (work done against friction)
(1/2) M V^2 = F * d
F is the friction force, which in this case is 0.25 M g. The 0.25 factor is the coefficient of kinetic friction.
Solve for the distance d. M cancels out.
d = (1/2) V^2/(0.25 g) = 2 V^2/g
1.84 m
To determine the distance you will slide before stopping, you can use the concept of kinetic friction and the equations of motion.
First, let's calculate the force of kinetic friction acting on you. The force of kinetic friction depends on the coefficient of friction (μ) and the normal force (N). In this case, the normal force is equal to your weight since you're standing on a horizontal surface.
The force of kinetic friction (ƒk) can be calculated as:
ƒk = μ * N
Next, we need to determine the normal force (N). The normal force acting on you is equal to your weight (mg), where m is your mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, let's determine the normal force (N). Since you're standing on a horizontal surface, the force of gravity (mg) is balanced by the normal force (N):
N = mg
Once we know the normal force (N), we can calculate the force of kinetic friction (ƒk) using the given coefficient of friction (μ = 0.250).
Now, let's calculate the force of kinetic friction:
ƒk = μ * N
Next, we can calculate the acceleration (a) using Newton's second law of motion, which states that the net force (ƩF) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
ƩF = ma
In this case, the net force is the force of kinetic friction (ƒk):
ƒk = ma
Lastly, we can use the equations of motion to determine the distance (d) you will slide before stopping. The equation that relates distance, initial velocity, final velocity, and acceleration is:
v^2 = u^2 + 2ad
where v is the final velocity (which is 0 m/s since you stop), u is the initial velocity (3.00 m/s), a is the acceleration (from the force of kinetic friction), and d is the distance.
By rearranging the equation, we can solve for d:
d = (v^2 - u^2) / (2a)
Now, let's put it all together and calculate the distance (d) you will slide before stopping.