Answer:
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Explanation:
To find the coefficient of static friction between the coin and the turntable, we can use the formula for centripetal force. The centripetal force is the force that keeps an object moving in a circular path.
First, we need to find the net force acting on the coin. The net force is the force required to keep the coin moving in a circular path. In this case, the net force is provided by the static friction between the coin and the turntable.
The formula for centripetal force is:
F = (m * v^2) / r
Where:
F is the net force
m is the mass of the coin (which we can assume to be constant)
v is the speed of the coin (120 cm/s in this case)
r is the distance of the coin from the center of the turntable (28 cm in this case)
Since the coin just begins to slip, we can set the static friction force equal to the centripetal force:
F_friction = (m * v^2) / r
The static friction force can be expressed as:
F_friction = μ * m * g
Where:
μ is the coefficient of static friction
g is the acceleration due to gravity (980 cm/s^2 in this case)
Now we can set the two expressions for the net force equal to each other:
(μ * m * g) = (m * v^2) / r
We can cancel out the mass (m) on both sides:
μ * g = (v^2) / r
Finally, we can solve for the coefficient of static friction (μ):
μ = ((v^2) / r) / g
Plugging in the given values:
μ = ((120 cm/s)^2 / 28 cm) / 980 cm/s^2
Simplifying this expression will give us the coefficient of static friction between the coin and the turntable.
