An ice skater moving at 10.0 m/s coast to a halt in 1.0 x 102 m on a smooth ice surface.
What is the coefficient of friction between the ice and the skates?
0.051
thz!!
Frictionwork=initial KE
mu*mg*distance=1/2 m v^2
solve for mu.
To find the coefficient of friction between the ice and the skates, we can use the equation:
frictional force = coefficient of friction * normal force
In this case, since the skater is coming to a halt, we know that the frictional force acting on the skater is equal to the force that stops the skater's motion. This force is the kinetic frictional force given by:
frictional force = mass * acceleration
where mass is the mass of the skater, and acceleration is the deceleration of the skater.
We can find the acceleration using the equation:
acceleration = (final velocity - initial velocity) / time
In this case, the initial velocity is 10.0 m/s, the final velocity is 0 m/s (since the skater comes to a halt), and the distance traveled is 1.0 x 10^2 m.
Plugging in the values, we have:
acceleration = (0 - 10.0) / (1.0 x 10^2)
Now, we can calculate the frictional force:
frictional force = mass * acceleration
To find the mass of the skater, we need the equation:
force = mass * gravity
The force is the skater's weight, and the normal force is equal to the skater's weight:
force = mass * gravity
Since the skater is not accelerating vertically, the normal force is equal to the skater's weight:
force = weight = mass * gravity
Now, we can calculate the frictional force:
frictional force = mass * acceleration
Finally, we can find the coefficient of friction using the equation:
coefficient of friction = frictional force / normal force
Plugging in the values, we can calculate the coefficient of friction between the ice and the skates.