while they are conducting the experiment they change the mass of the rubber stop

Question

while they are conducting the experiment they change the mass of the rubber stopper to the largest they can find, 0.50 kg. They also change the length of the string to 1.3 m. They note that this new mass causes the string to make a 10 degree angle from the horizontal.

a.cauluate the new force of tension

b. because these students never obtained their merit badges in boy scouts for knot tying, the string comes untied and the ball flies off towards the front of the classroom. caululate the speed of the ball when the string fails.

c.The instuctor at the front of the classroom receives the full impact of the ball to the right side of her face. She is .6m lower than the hight of the ball. Calculate how far away the instuctor is sitting.

Explanation / Answer

I believe that the enunciate of this question is incomplete, because it does not provide a value of speed or acceleration for the spinning of the stopper, we can only assume it. Considering this we have:

To calculate the new tension of the string, we need to know the centripetal force generated by the stopper while spinning. Thus we have:

F = T = m.a = (m.v2)/R

Where R is the new radios given by the length of the string and m is the mass of the stopper.

But because of the wheight of the stpper the string is now at a=10º the new tensión will be the horizontal component of the value of the total tension. Thus:

Tn = Tcos(a)

Assuming that the stopper is spinning at a constant acceleration, the speed at wich the string of the stopper fails is given by:

T= (m.v2)/R

v=sqrt(R/(T.m))

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