A hockey puck is sliding across a frozen pond with an initial speed of 6.5 m/s. It comes to rest after sliding a distance of 7.6 m. What is the coefficient of kinetic friction between the puck and the ice?

I know this one is not that difficult. However, I can't seem to get the correct answer. Any help is much apprectiated.

Initial puck kinetic energy

= work done against friction

(1/2) M V^2 = M*g*muk*X

muk is the coefficient of kinetic friction that you want. M cancels out, so you don't need to know it.

X is the distance that the puck slides while coming to a stop.

muk = (1/2) V^2/(g X)

That's all there is to it!

Ahh ok, I didn't realize the masses cancel out. But of course you're right.

That really was easy. :)

To find the coefficient of kinetic friction between the puck and the ice, we can use the equation:

friction force = coefficient of kinetic friction x normal force

In this case, the normal force is equal to the weight of the puck, which can be calculated using the formula:

weight = mass x acceleration due to gravity

First, we need to find the mass of the puck. We can use the equation:

force = mass x acceleration

Since the only force acting on the puck is the force of friction, we can write:

force = friction force

From the given information, we know the initial speed of the puck and the distance it slides before coming to rest. We can use the equation:

final velocity^2 = initial velocity^2 + 2 x acceleration x distance

Since the puck comes to rest, the final velocity is 0 m/s. Plugging in the given values, we have:

0 = (6.5 m/s)^2 + 2 x acceleration x 7.6 m

Solving for acceleration, we find:

acceleration = -((6.5 m/s)^2) / (2 x 7.6 m)

Now, we can find the mass of the puck using the equation:

force = mass x acceleration

The force is equal to the weight of the puck, so we have:

weight = mass x acceleration

Solving for mass, we find:

mass = weight / acceleration

Finally, we can substitute the mass and acceleration back into the equation for friction force:

friction force = coefficient of kinetic friction x weight

Solving for the coefficient of kinetic friction, we find:

coefficient of kinetic friction = friction force / weight

By plugging in the values we calculated, we can find the coefficient of kinetic friction between the puck and the ice.

given:mass m= 20 kilogram ,force = 50 N from newton 2nd law,

f=ma where a=acceleration of the box
a=f over m= 50 over 20=2.5