What Is the Coefficient of Kinetic Friction for a Hockey Puck on Ice?

[bbreezy]

I am having trouble with this problem, it states:
A hockey puck on a frozen pond with an initial speed of 14.1 m/s stops after sliding a distance of 198.9 m. Calculate the average value of the coefficient of kinetic friction between the puck and the ice.

I tried using the equation uk=a/g but didnt work out for me. Any help?

 

[cepheid]

Welcome to PF bbreezy!

Using basic kinematics, you can figure out what the object's acceleration must have been for it to require that stopping distance in order to come to rest from that initial speed.

Once you know the acceleration of the object, you know the net force on the object (due to Newton's second law). In this case, the net force is the frictional force, since it is the only one that acts on the object. So, equating the net force to the frictional force, you will indeed find that the expression you posted for the coefficient of friction is correct (since it will just turn out to be the ratio of the net force to the weight, and the m's will cancel).

So, if you didn't get the right answer, you must not have computed 'a' correctly. Can you post your calculations here?

 

[bbreezy]

Vi+2ad = 0
14.1+2(a)(198) = 0
2(a)(198) = -14.1

then this is where I think I am messing up

 

[cepheid]

Vi+2ad = 0
14.1+2(a)(198) = 0
2(a)(198) = -14.1

then this is where I think I am messing up

It should really be:

v_i² + 2ad = 0

 

[rwisz]

I would approach this problem by first identifying the known variables and then using appropriate equations to solve for the unknown variable.

In this case, we know the initial speed of the puck (14.1 m/s), the distance it travels (198.9 m), and we are trying to find the coefficient of kinetic friction between the puck and the ice. The equation we can use to solve for this is Ff = μkN, where Ff is the force of friction, μk is the coefficient of kinetic friction, and N is the normal force.

To find the normal force, we can use the equation N = mg, where m is the mass of the puck and g is the acceleration due to gravity (9.8 m/s^2). We can then substitute this into the first equation, along with the known distance and initial velocity, to solve for μk.

Therefore, the average value of the coefficient of kinetic friction between the puck and the ice is μk = Ff/N = (m*g*d)/N = (m*g*d)/(m*g) = d, where d is the distance traveled divided by the mass of the puck.

I would also like to note that using the equation uk=a/g would not be appropriate in this scenario as it is for calculating the coefficient of kinetic friction on an inclined plane, not on a flat surface like a frozen pond.

I hope this helps with solving the problem. If you continue to have trouble, I would recommend seeking assistance from a tutor or a colleague who may have more experience in this area.