HIGH SCHOOL STUDY HELP
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Can you explain to me how this question's answer is option 5?
Hi Alex,
Thank you for your question.
You may be wondering how to solve this question as the angle theta is not included in the question. However, you can solve the question like this:
1. As the mass is swinging in a horizontal circle at constant speed, this is an uniform circular motion type of question (horizontal circle).
2. So, only look at the horizontal force.
Key: ac = centripetal acceleration, T = Tension force
∑Fx = m(ac)
(Let the direction towards the center of the circle as positive)
Tsin(theta) = m(ac) = m(v^2)/r
***Remember: sin(theta) = opposite/hypotenuse = r/4r = 1/4
3. Solve for v
T/4 = m(v^2)/r
Tr/4m = v^2
v = sqrt(Tr/4m) = (1/2)(sqrt(Tr/m))
Hence, option 5 would be the correct answer.
Does that answer your question?
Hi Alex,
Thank you for your question.
You may be wondering how to solve this question as the angle theta is not included in the question. However, you can solve the question like this:
1. As the mass is swinging in a horizontal circle at constant speed, this is an uniform circular motion type of question (horizontal circle).
2. So, only look at the horizontal force.
Key: ac = centripetal acceleration, T = Tension force
∑Fx = m(ac)
(Let the direction towards the center of the circle as positive)
Tsin(theta) = m(ac) = m(v^2)/r
***Remember: sin(theta) = opposite/hypotenuse = r/4r = 1/4
3. Solve for v
T/4 = m(v^2)/r
Tr/4m = v^2
v = sqrt(Tr/4m) = (1/2)(sqrt(Tr/m))
Hence, option 5 would be the correct answer.
Does that answer your question?