How Long Can You Pull a Tablecloth Before a Glass Falls Off?

[physicsnoob93]

Homework Statement

If you have courage and a tight grip, you can yank a tablecloth from under the dishes on a table. What is the longest time in which the cloth can be pulled out so that a glass 6 in from the edge comes to rest before falling off the table? Assume that the coefficient of friction of the glass sliding on the tablecloth or sliding on the table top is 0.5.

Homework Equations

$$F_f=\mu mg$$

The Attempt at a Solution

Okay, so the force due to friction is $$F_f=\mu mg$$. The force will be applied for some maximum time: $$F_ft_{max}=\mu mgt_{max}$$. I'm not sure how to continue.

Thanks for your help.

 

[Doc Al]

Hint: What's the acceleration of the glass?

 

[nlightner]

Hello,

Thank you for your question. It is an interesting problem to consider the dynamics of a tablecloth being pulled out from under dishes on a table. In order to determine the maximum time in which the cloth can be pulled out so that a glass 6 inches from the edge comes to rest before falling off the table, we can use the equation F_f=\mu mg to calculate the maximum force of friction acting on the glass. Here, \mu is the coefficient of friction, which is given as 0.5, m is the mass of the glass, and g is the acceleration due to gravity.

To determine the maximum time, we need to consider the forces acting on the glass. The only forces acting on the glass are the force of gravity, mg, and the force of friction, F_f. Since we want the glass to come to rest before falling off the table, the maximum force of friction must be equal to or greater than the force of gravity, mg. Therefore, we can write the following inequality:

F_f \geq mg

Substituting in the expression for F_f, we get:

\mu mg \geq mg

Simplifying, we get:

\mu \geq 1

Since the coefficient of friction cannot be greater than 1, we can conclude that the maximum force of friction must be equal to the force of gravity, mg.

Now, we can use the equation F_ft_{max}=\mu mgt_{max} to calculate the maximum time, t_{max}. Substituting in the value of \mu and rearranging the equation, we get:

t_{max} = \frac{1}{\mu g}

Plugging in the value of \mu=0.5 and the acceleration due to gravity, g=9.8 m/s^2, we get:

t_{max} = \frac{1}{0.5\times9.8} \approx 0.204 seconds

Therefore, the longest time in which the cloth can be pulled out so that the glass comes to rest before falling off the table is approximately 0.204 seconds.

I hope this helps. Let me know if you have any further questions.

Best,