Centripetal Motion + Friction = Impossible?

[bfr]

Homework Statement

1.
An air puck of mass .25 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of
2.
the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it. The suspended mass remains in equilibrium while the puck on the tabletop revolves.
3.

4.
a. What is the tension in the string? Answer: 9.8
5.
b. What is the speed of the puck? Answer:: 6.26
6.
c. If the table is not frictionless, but instead is made of a material with a coefficient of friction u=0.45, how do your answers for a) and b) change? (answer: ?)

Homework Equations

v=(2*pi*R)/T
a=(v^2)/R

The Attempt at a Solution

I'm not sure. How would the situation even apply? (I only need help with part c).

 

[anathema]

Hello,

Thank you for your post. I can help you with part c of the problem.

First, let's review the given information. We have an air puck with a mass of 0.25 kg tied to a string and revolving in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string is tied to a mass of 1.0 kg, which remains in equilibrium while the puck revolves. We have also been given the values for the tension in the string (9.8 N) and the speed of the puck (6.26 m/s).

Now, let's consider the effect of friction on the system. Friction is a force that opposes motion between two surfaces in contact. In this case, the friction between the air puck and the table will act in the opposite direction of the puck's motion, slowing it down. This means that the speed of the puck will decrease, and the tension in the string will increase.

To calculate the new tension in the string, we can use the formula for the net force acting on the puck:

F_net = ma = T - F_friction

Where F_net is the net force, m is the mass of the puck, a is the acceleration of the puck, T is the tension in the string, and F_friction is the force of friction.

We can rearrange this equation to solve for the new tension:

T = ma + F_friction

We already know the values for m and a, so we just need to calculate the force of friction. The force of friction can be calculated using the coefficient of friction (u) and the normal force (F_normal). The normal force is the force exerted by the table on the puck, which is equal to the weight of the puck (mg).

F_friction = u*F_normal = u*mg

Substituting this into our previous equation, we get:

T = ma + u*mg

Now, we can plug in the values for m, a, u, and g to calculate the new tension:

T = (0.25 kg)(6.26 m/s^2) + (0.45)(0.25 kg)(9.8 m/s^2)

T = 1.565 N + 1.1025 N

T = 2.6675 N

So, the new tension in the string is 2.

 

[Moetasim]

I would like to clarify that the statement "Centripetal Motion + Friction = Impossible?" is not entirely accurate. While friction can certainly affect the motion of an object in a circular path, it does not necessarily make it impossible.

In this particular scenario, the presence of friction on the tabletop will cause the air puck to slow down and eventually stop moving in a circular path. This is because friction acts in the opposite direction of motion, causing a deceleration. However, the suspended mass will still remain in equilibrium due to the tension in the string.

To answer part c of the question, we need to take into account the effect of friction on the speed and tension. Friction will cause the speed of the puck to decrease, as it is constantly acting to slow it down. The new speed can be calculated using the equation v= (2*pi*R)/T, where T is the new time period due to the decrease in speed.

The presence of friction will also affect the tension in the string. The tension will now have to not only balance the weight of the suspended mass, but also provide enough force to overcome the friction and maintain the circular motion. This can be calculated using the equation a=(v^2)/R, where a is the centripetal acceleration and v is the new speed calculated above.

So, in summary, the answers for part a and b will change because of the presence of friction. The tension in the string will increase and the speed of the puck will decrease. It is important to note that while friction does make it more challenging to maintain circular motion, it is not impossible. Many real-world scenarios involve the combination of centripetal motion and friction, and engineers and scientists work to find ways to minimize its effects.