A coin is placed 33 cm from the center of a
horizontal turntable, initially at rest. The
turntable then begins to rotate. When the
speed of the coin is 100 cm/s (rotating at a
constant rate), the coin just begins to slip.
The acceleration of gravity is 980 cm/s2 .
What is the coefficient of static friction be-
tween the coin and the turntable?
To find the coefficient of static friction between the coin and the turntable, we can use the following steps:
1. Identify the forces acting on the coin:
- Force due to gravity (weight): W = mg, where m is the mass of the coin and g is the acceleration due to gravity.
- Normal force (N): The force exerted by the turntable on the coin perpendicular to the surface of contact.
- Frictional force (f): The force opposing the motion of the coin.
2. Determine the net force acting on the coin:
The net force acting on the coin can be found by considering the forces in the radial direction. We know that the centripetal force acting on the coin is provided by the frictional force, so we have:
f = m * ac, where ac is the centripetal acceleration of the coin.
3. Calculate the centripetal acceleration:
The centripetal acceleration can be calculated using the equation:
ac = (v^2) / r, where v is the velocity of the coin and r is the distance of the coin from the center of the turntable.
4. Substitute the values into the equations:
- Net force: f = m * ac = m * (v^2) / r
- Frictional force: f = μs * N, where μs is the coefficient of static friction.
5. Solve for the coefficient of static friction (μs):
μs = (m * (v^2) / r) / N
Let's calculate the coefficient of static friction using the given values:
- Distance from the center of the turntable (r) = 33 cm
- Velocity of the coin (v) = 100 cm/s
- Acceleration due to gravity (g) = 980 cm/s^2
Take note that we still need to find the value of the normal force (N). To do this, we can use the equation:
N = m * g
Now we can substitute the values into the equation to find the coefficient of static friction.