During the Olympic ice competition, Boris (m = 75 kg) glides at 1.8 m/s to a stationary Juliette (52 kg) and hangs on. How far will the pair slide after the collision if the coefficient of kinetic friction between the ice and their skates is .042?
get V from momentum
(75 + 52) V = 75 (1.8)
calculate V
calculate (1/2) m V^2
friction force = .042 * m * g
friction force * distance = (1/2) m V^2
or actually m cancels
.042 g d = .5 V^2
To find the distance the pair will slide after the collision, we need to determine the stopping force acting on them and then use it to calculate the distance.
First, let's calculate the force of friction acting on the pair. The formula for calculating frictional force is:
Force of friction = coefficient of friction * normal force
The normal force is the force exerted by the surface perpendicular to it, which is equal to the weight of the person or object. However, since Boris and Juliette are hanging on to each other, the normal force acting on them is only equal to the weight of Boris.
The weight of Boris can be calculated by multiplying his mass by the acceleration due to gravity:
Weight of Boris = mass of Boris * acceleration due to gravity
Weight of Boris = 75 kg * 9.8 m/s^2
Next, we can calculate the force of friction:
Force of friction = coefficient of friction * normal force
= 0.042 * (75 kg * 9.8 m/s^2)
Now, we have the force of friction acting on Boris and Juliette. We can use this force to calculate the distance they will slide.
The work done by friction to stop the pair can be calculated using the work-energy principle:
Work done by friction = force of friction * distance
Since the work done by friction results in a loss of kinetic energy, it can be equated to the initial kinetic energy:
Work done by friction = (1/2) * (mass of Boris + mass of Juliette) * (final velocity)^2
Since the final velocity is zero (they stop), we can simplify the equation:
Work done by friction = (1/2) * (mass of Boris + mass of Juliette) * (0)^2
= 0
Setting the work done by friction equal to zero, we can solve for the distance:
(Force of friction) * distance = 0
distance = 0 / (Force of friction)
Therefore, the distance the pair will slide after the collision is zero.