What coefficient of friction is required to stop a hockey puck sliding at 12.8 m/s initially over a distance of 66.5 m?
KE = W(fr)
m•v²/2 = μ•m•g•s,
μ = v²/2• g•s
To determine the coefficient of friction required to stop a hockey puck, we can use the concept of work and energy. The work done by friction will be equal to the change in the puck's kinetic energy.
The kinetic energy (KE) of the hockey puck can be calculated using the formula:
KE = (1/2) * m * v^2
Where:
KE = kinetic energy
m = mass of the hockey puck
v = velocity of the hockey puck
Given:
Initial velocity, v = 12.8 m/s
Distance traveled, d = 66.5 m
Firstly, we need to find the time it takes for the hockey puck to stop. We can use the equation of motion:
v^2 = u^2 + 2ad
Where:
u = initial velocity
a = acceleration
d = distance traveled
Rearranging the equation, we get:
a = (v^2 - u^2) / (2d)
Plugging in the values, we have:
a = (0^2 - 12.8^2) / (2 * 66.5)
Calculating this, we find:
a ≈ -16.2 m/s^2
The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, which is expected since the puck is slowing down.
Now, we can use the equation:
Work = Force * Distance
The force of friction (F) can be represented as:
F = μ * m * g
Where:
μ = coefficient of friction
g = acceleration due to gravity (approximately 9.8 m/s^2)
The work done by friction is equal to the force of friction multiplied by the distance traveled:
Work = F * d
Since the work done by friction is equal to the change in kinetic energy, we have:
F * d = (1/2) * m * (0^2 - 12.8^2)
Substituting the values, we get:
μ * m * g * d = (1/2) * m * (-12.8^2)
The mass of the hockey puck cancels out, and we can rearrange the equation to solve for the coefficient of friction (μ):
μ = (1/2) * (-12.8^2) / (g * d)
Plugging in the values, we have:
μ ≈ (1/2) * (-12.8^2) / (9.8 * 66.5)
Calculating this, we find:
μ ≈ -0.383
The coefficient of friction required to stop the hockey puck is approximately -0.383. Note that the negative sign indicates that the friction force is acting in the opposite direction to the motion of the puck.
To find the coefficient of friction required to stop a hockey puck sliding, we can use the work-energy principle. According to this principle, the work done on an object is equal to its change in kinetic energy.
The work done on the puck can be calculated from the force of friction, which is given by the equation:
Frictional force (F) = coefficient of friction (μ) * normal force (N)
The normal force is equal to the weight of the puck, which can be calculated by multiplying the mass of the puck (m) by the acceleration due to gravity (g):
Normal force (N) = m * g
The work done by the frictional force over a distance (d) is given by:
Work (W) = F * d
Since the work done by the frictional force results in a change in kinetic energy, we can equate the work to the initial kinetic energy of the puck:
W = ΔKE = 0 - 0.5 * m * v^2
where v is the initial velocity of the puck.
Combining these equations, we can solve for the coefficient of friction (μ):
μ * m * g * d = -0.5 * m * v^2
μ = (-0.5 * m * v^2) / (m * g * d)
Now, let's plug in the given values:
- Initial velocity (v) = 12.8 m/s
- Distance (d) = 66.5 m
- Acceleration due to gravity (g) = 9.8 m/s^2 (approximately)
μ = (-0.5 * m * (12.8)^2) / (m * (9.8) * 66.5)
First, you need to find the mass of the hockey puck. If the mass is not given, you can refer to the specifications of the standard hockey puck, which is approximately 0.16 kg.
μ = (-0.5 * 0.16 * (12.8)^2) / (0.16 * (9.8) * 66.5)
Simplify the equation:
μ = (-0.5 * 0.16 * 163.84) / (0.16 * 646.7)
μ = -13.1072 / 103.472
μ ≈ -0.1264
The coefficient of friction required to stop the hockey puck sliding is approximately -0.1264. Note that the negative sign indicates that the force of friction is opposite to the direction of motion.