A 90kg basketball player carries about 720J of kinetic energy when running down the court. If the coefficient of kinetic friction between good runners & the floor is .600, how far does the player skid when trying to stop? Hint: what work was done by friction in bringing the player to a stop?
I am so at a loss with where to go... I used Ek=1/2mV^2 to get my velocity which is 4m/s but where do I go from there?
Thanks! :)
the friction/work hint is a good one
90 * g * .6 * d = 720
I don't think I have that formula... So mg(mu)d=Ek? making d=190.8 then I can use kinematics to get a & w=mad? :) thanks a ton :)
To determine the distance the player skids when trying to stop, we can use the work-energy theorem. According to the theorem, the work done on an object is equal to the change in its kinetic energy.
In this case, the initial kinetic energy (Ek1) is given as 720 J, which corresponds to the player running down the court. The final kinetic energy (Ek2) is zero because the player comes to a stop.
We can calculate the work done by friction (W) to bring the player to a stop by using the following equation:
W = Ek2 - Ek1
Since Ek2 is zero, the equation simplifies to:
W = -Ek1
Now, the work done by friction can be determined by multiplying the force of friction (F) by the distance traveled (d):
W = F * d
The force of friction (F) can be calculated using the equation:
F = μ * m * g
Where μ is the coefficient of kinetic friction (0.600), m is the mass of the player (90 kg), and g is the acceleration due to gravity (9.8 m/s^2).
Substituting the values into the equation, we get:
F = (0.600) * (90 kg) * (9.8 m/s^2) = 529.2 N
Now, we can substitute the value of F into the work equation to solve for distance (d):
W = F * d
-720 J = (529.2 N) * d
Solving for d, we get:
d = -720 J / (529.2 N) ≈ -1.36 m
Since distance cannot be negative, we take the absolute value to get the positive value of distance:
d ≈ 1.36 m
Therefore, the player skids for approximately 1.36 meters when trying to stop.
To find the distance the basketball player skids when trying to stop, you can start by calculating the work done by friction to bring the player to a stop. Here's how you can proceed:
Step 1: Calculate the velocity of the basketball player using the given kinetic energy equation:
Kinetic energy (KE) = 1/2 * mass (m) * velocity (v)^2
Substituting the given values:
720J = 1/2 * 90kg * v^2
Solving for the velocity (v):
720J = 45kg * v^2
v^2 = 720J / 45kg
v^2 = 16
v = √16
v = 4m/s
So, you correctly calculated the velocity of the basketball player as 4m/s.
Step 2: The work done by friction (W_friction) is equal to the force of friction (F_friction) multiplied by the distance (d) over which the player skids. However, you need to determine the force of friction first.
The force of friction (F_friction) can be calculated using:
F_friction = coefficient of kinetic friction (μ) * normal force (N)
The normal force (N) is equal to the weight of the player, which can be found using:
Weight (W) = mass (m) * gravitational acceleration (g)
Given: mass (m) = 90kg and gravitational acceleration (g) = 9.8m/s^2
Substituting these values:
Weight (W) = 90kg * 9.8m/s^2
W = 882N
The normal force (N) is equal to the weight (W):
N = 882N
Now, substitute the coefficient of kinetic friction (μ) and the normal force (N) into the equation for force of friction (F_friction):
F_friction = 0.600 * 882N
F_friction = 529.2N
Step 3: Now, we can calculate the work done by friction using the formula:
Work (W) = Force (F) * distance (d)
Given: Force (F) = F_friction = 529.2N
To find the distance (d), we need to rearrange the equation:
Distance (d) = Work (W) / Force (F_friction)
Substituting the given values:
Distance (d) = 720J / 529.2N
Distance (d) ≈ 1.360m
Therefore, the basketball player skids approximately 1.360 meters when trying to stop.
Remember, to solve such problems, always start with the relevant equations and substitute the given values accurately.