What coefficient of friction is required to stop a hockey puck sliding at 12.3 m/s initially over a distance of 38.7 m?

Well, in a game of hockey, I could definitely imagine a lot of slippery situations. But let me crunch some numbers to answer your question about coefficients of friction!

To calculate the coefficient of friction, we need to use the equation:

friction force = coefficient of friction * normal force

Now, in this case, we don't have the normal force given. However, if we assume that the hockey puck is on a horizontal surface, we can say that the normal force is equal to the weight of the puck.

When we stop the puck, it means that the friction force is equal to the force that was initially sliding the puck. In other words:

friction force = force that was sliding the puck

The force that was sliding the puck can be calculated using the equation:

force = mass * acceleration

Since we're just looking for the coefficient of friction, we don't need to know the actual mass of the hockey puck.

So, let's put it all together. We have:

friction force = coefficient of friction * normal force
force = mass * acceleration

Since friction force = force, we can set them equal to each other:

coefficient of friction * normal force = mass * acceleration

Now, let's rearrange the equation to solve for the coefficient of friction:

coefficient of friction = (mass * acceleration) / normal force

Without the mass and the normal force given, I'm afraid I can't provide an exact numerical answer. However, I hope the steps I laid out help guide you to find the coefficient of friction you're looking for. And remember, if all else fails, just blame the ice for being too slippery!

To find the coefficient of friction required to stop a hockey puck sliding at a certain initial velocity and distance, we can use the equations of motion for constant acceleration.

The equation we will use is:

v^2 = u^2 + 2as

Where:
- v is the final velocity (0 in this case, as we want to stop the puck)
- u is the initial velocity (12.3 m/s)
- a is the acceleration (which is due to the friction)
- s is the distance traveled (38.7 m)

Rearranging the equation to solve for the acceleration:

0^2 = (12.3)^2 + 2a(38.7)

0 = 151.29 + 77.4a

Subtracting 151.29 from both sides:

77.4a = -151.29

Dividing by 77.4:

a = -1.956 m/s^2

The negative sign indicates that the acceleration is opposite to the initial velocity, which means it is due to the friction slowing down the puck.

The coefficient of friction can be found using the equation:

μ = a/g

Where:
- μ is the coefficient of friction
- a is the acceleration
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Substituting the known values:

μ = -1.956 / 9.8

μ = -0.1998

Therefore, the coefficient of friction required to stop the hockey puck sliding at 12.3 m/s initially over a distance of 38.7 m is approximately -0.1998. Note that the negative sign indicates that the friction force opposes the puck's motion.

To find the coefficient of friction required to stop the hockey puck, we need to use the equation for the force of friction. The force of friction can be calculated using the equation:

Frictional Force = coefficient of friction * Normal Force

In this case, the normal force is equal to the weight of the hockey puck, which can be determined using the equation:

Weight = mass * acceleration due to gravity

We can assume the mass of the puck remains constant, however, the weight will change over time due to the decreasing speed of the puck as it comes to a stop. To find the force of friction, we also need to consider the equation for acceleration:

Acceleration = Change in velocity / Time

Since our goal is to stop the puck, the final velocity will be zero. We can rearrange the equation to solve for time:

Time = Change in velocity / Acceleration

Now, let's calculate the force of friction:

1. Calculate the weight of the hockey puck:
- Determine the mass of the puck (if not given).
- Multiply the mass by the acceleration due to gravity (approximated as 9.8 m/s^2) to find the weight.

2. Calculate the time it takes to stop:
- The initial velocity is given as 12.3 m/s.
- The final velocity is 0 m/s (since we want to stop the puck).
- Use the equation: Time = Change in velocity / Acceleration.

3. Calculate the force of friction:
- Rearrange the equation to solve for the force of friction:
Frictional Force = mass * acceleration.
- Substitute the mass and acceleration values from step 1.

4. Find the coefficient of friction:
- Use the equation: Frictional Force = coefficient of friction * Normal Force.
- Rearrange the equation to solve for the coefficient of friction:
coefficient of friction = Frictional Force / Normal Force.

By following these steps, you can determine the coefficient of friction required to stop the hockey puck sliding at the given initial velocity and distance.