Solving Circular Motion: Find Time & Position of Breaking String

[fenixxishot]

All right i have a big test on monday in physics and the only thing my proffesor gave to me to study was this and i really don't know where to begin

A boy spins a 5kg mass on a string of length 1.3 meters. He initially spins it with a constant linear velocity of 4m/s. At time=0 , it is at 3pi/4 radians, and he begins to give it a constant angular acceleration of a = .8rad/s/s. The maximum tension the string can withstand without breaking is 230N.

At what time will the string break? at what position will the mass be when this happens?

He does give a hint which to my closed mind does not help (w=v/r , a=w^2(r)

Ohh i think he said that is was spining vertically not horizontally
Thanks for you time

 

[Pyrrhus]

Start by writing down the data, and the kinematic equations (radial acceleration) for circular motion in curvilinear coordinates. Now start by analyzing the case when t=0.

 

[kyle8921]

To solve this problem, we can use the equations of circular motion. First, we need to find the angular velocity (w) of the mass, which is equal to the linear velocity (v) divided by the radius (r) of the circular motion. In this case, v=4m/s and r=1.3m, so w=4/1.3=3.077 rad/s.

Next, we can use the equation a=w^2(r) to find the angular acceleration (a) of the mass. Plugging in the values, we get a=(3.077)^2(1.3)=12.6 rad/s^2.

Now, we can use the equation for tension in circular motion, T=m(w^2)r, to find the tension in the string at any given time. Since the maximum tension the string can withstand is 230N, we can set up the following equation:

230=m(3.077)^2(1.3)

Solving for m, we get m=5.6kg. This means that the mass will break the string when its mass is 5.6kg.

To find the time when this will happen, we can use the equation for angular displacement (θ=θ0+w0t+1/2at^2) and set it equal to 3pi/4 radians, since this is the initial angular position of the mass. We can solve for t and get t=0.339 seconds.

At this time, the mass will be at its initial position of 3pi/4 radians. This means that the string will break when the mass is at the top of its circular motion.

In summary, the string will break at 0.339 seconds and the mass will be at 3pi/4 radians when this happens. It is important to note that this solution assumes that the string is being spun in a vertical circular motion. If it is being spun horizontally, the equations and solution may differ. I hope this helps with your studying and good luck on your test!