A hockey puck on a frozen pond is given an initial speed of 20.0 m/s. If the puck always
remains on the ice and slides 115 m before coming to rest, determine the coefficient of
kinetic friction between the puck and ice. (Answer: = 0.177 k
μ )
To find the coefficient of kinetic friction between the puck and ice, we need to use the equation for the work done by friction.
The work done by friction is given by the equation:
Work = Force * Distance * cosθ
Where:
- Work is the work done by friction (which is equal to the change in kinetic energy),
- Force is the force of friction,
- Distance is the distance the puck slides, and
- θ is the angle between the force of friction and the direction of motion.
In this case, the puck is sliding horizontally, so the angle between the force of friction and the direction of motion is 0°, and cosθ = 1.
We know that work done by friction is equal to the change in kinetic energy. So, we can write the equation as:
Force * Distance = 1/2 * mass * (final velocity^2 - initial velocity^2)
We are given that the initial speed of the puck is 20.0 m/s and it slides a distance of 115 m before coming to rest. Also, the mass of the puck cancels out in the equation, so we don't need it. Let's plug in the values:
Force * 115 = 1/2 * (0^2 - 20^2)
Simplifying the equation:
Force * 115 = -1/2 * 400
Force * 115 = -200
Dividing both sides by 115:
Force = -200 / 115
Force = -1.739 m/s²
Now, we can use the formula for force of friction:
Force of friction = coefficient of kinetic friction * Normal force
The normal force is the force exerted on the puck by the ice and is equal to the weight of the puck, which is m * g.
To find the force of gravity (weight), we need to know the mass of the puck. Let's assume it is 1 kg for simplicity. The acceleration due to gravity is 9.8 m/s².
Weight = m * g = 1 kg * 9.8 m/s² = 9.8 N
Now, let's substitute the values back into the equation for the force of friction:
-1.739 m/s² = coefficient of kinetic friction * 9.8 N
Dividing both sides by 9.8:
coefficient of kinetic friction = -1.739 / 9.8
coefficient of kinetic friction ≈ -0.177
However, the coefficient of friction should be a positive value. Since the frictional force always opposes motion, its direction is opposite to that of the applied force. So, we take the absolute value of the coefficient of kinetic friction:
coefficient of kinetic friction ≈ 0.177
Therefore, the coefficient of kinetic friction between the puck and ice is approximately 0.177.
To determine the coefficient of kinetic friction, we need to use the equation that relates the distance traveled by an object, the initial velocity, the coefficient of kinetic friction, and other known factors.
The equation we can use is:
d = v^2 / (2μg)
where:
d is the distance traveled by the object (115 m in this case),
v is the initial velocity of the object (20.0 m/s in this case),
μ is the coefficient of kinetic friction (which we need to find),
and g is the acceleration due to gravity (approximately 9.8 m/s^2).
To solve for μ, we need to rearrange the equation:
μ = v^2 / (2gd)
Now we can substitute the given values:
μ = (20.0 m/s)^2 / (2 * 9.8 m/s^2 * 115 m)
Calculating this, we find:
μ ≈ 0.177
Therefore, the coefficient of kinetic friction between the puck and ice is approximately 0.177.
Work done against friction = Initial kinetic energy
M*g*ì*X = (M/2) Vo^2
ì = Vo^2/(2 g X)