A coin rests on a record 0.15 m from its center. The record turns on a turntable that rotates at variable speed. The coefficient of static friction between the coin and the record is 0.30.

What is the maximum coin speed at which it does not slip?

static =velocity squared over (radius times gravity). solve for velocity and you get velocity to equal square root (radius*gravity*static)=square root of .15*.30*9.8= .664 m/s

Well, this is quite the spinning situation, isn't it? The coefficient of static friction between the coin and the record is 0.30, meaning that it needs to overcome this force to start slipping. The maximum speed at which the coin does not slip is when the friction force equals the centripetal force.

To find this, we need to remember that the centripetal force is given by the equation Fc = mv²/r, where m is the mass of the coin, v is its velocity, and r is the distance from the center of rotation.

Since we're dealing with static friction here, we can say that the maximum friction force is equal to μN, where μ is the coefficient of static friction and N is the normal force. In this case, the normal force is equal to the weight of the coin, N = mg.

Now, we can set up the equation: μN = mv²/r

Replacing N with mg, we get: μmg = mv²/r

Simplifying, we find that v² = μg⋅r

Finally, taking the square root of both sides, we have v = √(μg⋅r)

Plugging in the given values: μ = 0.30, g = 9.8 m/s², and r = 0.15 m, we can calculate the maximum velocity of the coin without slipping.

v = √(0.30 * 9.8 * 0.15) = 0.73 m/s

So, the maximum speed at which the coin does not slip is approximately 0.73 m/s. Just don't get too dizzy trying to calculate it!

To determine the maximum coin speed at which it does not slip, we need to consider the balance of forces acting on the coin.

The maximum speed occurs when the force of static friction reaches its maximum value, which is given by the equation:

F_static_friction = coefficient_of_static_friction * normal_force

The normal force in this case is equal to the weight of the coin, which is the force due to gravity acting on it. The weight is given by:

Weight = mass * acceleration_due_to_gravity

Assuming the mass of the coin is known, and the acceleration due to gravity is approximately 9.8 m/s^2, we can proceed to calculate the normal force:

Normal_force = mass * acceleration_due_to_gravity

Now, the maximum force of static friction is equal to the centripetal force acting on the coin, which is given by:

Centripetal_force = mass * velocity^2 / radius

where radius is the distance from the center of the coin to the axis of rotation (0.15 m in this case).

Setting the maximum force of static friction equal to the centripetal force, we can solve for the maximum velocity:

coefficient_of_static_friction * normal_force = mass * velocity^2 / radius

Simplifying the equation, we get:

velocity^2 = (coefficient_of_static_friction * normal_force * radius) / mass

Taking the square root of both sides:

velocity = sqrt((coefficient_of_static_friction * normal_force * radius) / mass)

Now, plug in the known values for the coefficient of static friction, radius, mass, and acceleration due to gravity, and calculate the maximum coin speed:

velocity = sqrt((0.30 * (mass * acceleration_due_to_gravity) * 0.15) / mass)

The mass cancels out:

velocity = sqrt(0.30 * acceleration_due_to_gravity * 0.15)

Substituting the value for the acceleration due to gravity, we get:

velocity = sqrt(0.30 * 9.8 * 0.15)

Calculating the square root:

velocity ≈ sqrt(0.441)

velocity ≈ 0.664 m/s

Therefore, the maximum coin speed at which it does not slip is approximately 0.664 m/s.

To find the maximum coin speed at which it does not slip, we need to consider the forces acting on the coin and determine the conditions for static friction to hold.

The coin is subject to two forces: the force of gravity acting downward and the static friction force acting inward, towards the center of the record.

The maximum speed at which the coin does not slip occurs when the static friction force is equal to the maximum static friction force, denoted as "fs_max". The maximum static friction force can be calculated using the equation:

fs_max = μs * N

where μs is the coefficient of static friction and N is the normal force.

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

N = m * g

where m is the mass of the coin and g is the acceleration due to gravity.

Assuming the mass of the coin is known, we can calculate the normal force using the mass and the value of g (approximately 9.8 m/s^2). Then we can find the maximum static friction force (fs_max) using the coefficient of static friction.

Once we have the value of fs_max, we can equate it to the centripetal force acting on the coin, which is given by:

fc = m * a_c

where m is the mass of the coin and ac is the centripetal acceleration, given by:

ac = v^2 / r

where v is the velocity of the coin and r is the distance from the center of the record to the coin.

Since fs_max = fc, we can rearrange the equations to solve for the maximum speed:

μs * N = m * (v^2 / r)

Using the values you provided and the equation above, we can substitute the known values and solve for the maximum speed (v).

I'll calculate it for you, give me a moment.