Question

A toy cart at the end of a string 0.70 m long moves in a circle on a table. The cart has a mass of 2.0 kg and the string has a breaking strength of 40. N. Calculate the maximum speed the cart can attain without breaking the string.

Answer 1

First off you would want to start off drawing a diagram and label the forces acting on the cart, although this isn't always mandatory, I find it extremely helpful. Then you are going to want to find the Sum of all the forces acting on the cart and set it equal to mass x acceleration. Then you are going to want to substitute in \[\frac{ v^2 }{r}\] for the acceleration because the forces are centripetal, therefore you want to calculate the centripetal acceleration. You should then have the equation \[T-(mg)=m \frac{ v^2 }{ r }\] Where T is the maximum tension, or breaking strength, (mg) is the mass x gravity or the weight, m is mass, v is velocity, and r is the radius, or the length of the string.
Finally you plug in all of your numerical values and solve for v.

I hope this helped

Answer 2

mg has nothing to do with this problem

Answer 3

draw a FBD of the car and apply Newtons second Law