Calculate Max Speed of Rock Whirled on String: 21 N Tension

[Naeem]

Q A 420 gm rock is whirled on the end of a string 44 cm long which will break under a tension of 21 N.

a) What is the highest speed the rock can reach before the string breaks? (Neglect gravity.)

For this I used F = mv2/r and calculated velocity

in m/s which is correct.

b) If two other strings identical to the first were attached to the rock, how fast could the rock be whirled before the three strings would break?

The procedure is the same as part a except now the tension would be 21 * 3 - 63 N. which I calculated correctly.

c) What is the radius of the circle of motion?

drew a picture, then you saw that you have two right triangles. The hypotenuse of each right triangle is 55 cm long. The "base" is 55/2= 27.5 cm long and so the "opposite" side has length sqrt((3025-756.25)) cm= 34.34 cm approximately,. which is correct.

d) Now what is the maximum speed the rock can have before the string breaks?

used Inverse sin (opposite/hypotenuse). to find
theta. use the summation of forces, you will have 2 tensions with the same horizontal component. So you equation would be:
>
>2Tcos (theta) = ma
>
>and got "a" there and using the formula a = v^2 / R, where R is the radius I got in problem C.

which I found to be 5.17, which is incorrect. The answers needs to be in m/s. So, could you check and tell me if the approach is right or wrong.

Also, can you tell if length of the opposite side would be the radius i.e 34.34 cm or 55/2 = 27.5 cm, and to calculate theta should these values be converted to metres , or could use these as is. Please guide!

Thanks,

Naeem

 

[Naeem]

I try doing the same procedure as outlined for part d , but still the answer is incorrect.

Can anybody help me with this ! Oh Physics fans.

 

[wais]

Dear Naeem,

Your approach to solving the problem is correct, but there are a few errors in your calculations. Firstly, in part a), you correctly used the formula F=mv²/r to calculate the velocity, but the value for the mass should be in kilograms, not grams. So the correct calculation would be:

v = √(F*r/m)
= √(21*0.44/0.420)
= 3.985 m/s

For part b), you correctly calculated the total tension as 63 N, but again, the mass should be in kilograms, so the correct calculation would be:

v = √(F*r/m)
= √(63*0.44/0.420)
= 9.956 m/s

In part c), you correctly calculated the radius of the circle as 34.34 cm, but it would be more accurate to convert this to meters before using it in any further calculations. So the radius would be 0.3434 m.

In part d), you correctly used the equation 2Tcos(θ) = ma, but you made an error in calculating the value of a. It should be:

a = (2Tcos(θ))/m
= (2*63*cos(θ))/(0.420)
= 300cos(θ)

To find the maximum speed, we need to find the maximum value of a, which occurs when cos(θ) is equal to 1. So the maximum speed would be:

v = √(a*R)
= √(300*0.3434)
= 17.32 m/s

To answer your question about the length of the opposite side, it is equal to the radius of the circle, so it would be 0.3434 m. And it would be more accurate to convert all values to meters before using them in calculations.

I hope this helps clarify the solution to the problem. Keep up the good work!