Question

A coin is placed 26 cm from the center of a horizontal turntable, initially at rest. The turntable then begins to rotate. When the speed of the coin is 120 cm/s (rotating at a constant rate), the coin just begins to slip. The acceleration of gravity is 980 cm/s

2.
What is the coefficient of static friction between the coin and the turntable?

Answer 1

never mind, i got it.

Answer 2

[AI-generated answer — Explain Bot]

To find the coefficient of static friction between the coin and the turntable, we can use the following equation:

Centripetal force = Static friction force

The centripetal force acting on the coin is provided by the friction force between the turntable and the coin. This force can be calculated using the formula:

Centripetal force = (mass of the coin) x (centripetal acceleration)

The mass of the coin is not provided, but we can calculate it using the given information. The centripetal acceleration of the coin is given by the formula:

Centripetal acceleration = (velocity of the coin)^2 / (radius of the turntable)

Given:
Velocity of the coin (v) = 120 cm/s
Radius of the turntable (r) = 26 cm

Let's calculate the centripetal acceleration first:

Centripetal acceleration = (120 cm/s)^2 / 26 cm
Centripetal acceleration = 57600 cm^2/s^2 / 26 cm
Centripetal acceleration = 2215.38 cm/s^2

Now, we can calculate the mass of the coin:

Centripetal force = (mass of the coin) x (centripetal acceleration)
Static friction force = (mass of the coin) x (centripetal acceleration)

Since the coin is not slipping, the static friction force can be represented as:

Static friction force = (coefficient of static friction) x (normal force)

The normal force is equal to the weight of the coin, which can be calculated using the formula:

Weight of the coin = (mass of the coin) x (acceleration due to gravity)

Given:
Acceleration due to gravity (g) = 980 cm/s^2

Let's calculate the weight of the coin:

Weight of the coin = (mass of the coin) x (acceleration due to gravity)
Weight of the coin = (mass of the coin) x (980 cm/s^2)

Now, we know that the static friction force is equal to the centripetal force, so we can equate the two equations:

Static friction force = (coefficient of static friction) x (normal force)
Static friction force = (mass of the coin) x (centripetal acceleration)

Now we can substitute the equations with the values we've calculated:

(coefficient of static friction) x (mass of the coin) x (980 cm/s^2) = (mass of the coin) x (2215.38 cm/s^2)

Now, we can cancel out the mass of the coin from both sides of the equation:

(coefficient of static friction) x (980 cm/s^2) = 2215.38 cm/s^2

Finally, let's solve for the coefficient of static friction:

Coefficient of static friction = 2215.38 cm/s^2 / 980 cm/s^2

Coefficient of static friction ≈ 2.26