A ball with mass m=1.72 kg is attached to a peg at point C using a length of mas

Question

A ball with mass m=1.72 kg is attached to a peg at point C using a length of massless string of L=1.54m. It is released from the top of a vertical circle (gravity points down on the page) with speed v=4.01m/s as shown in the figure. Defining the angle as shown, what is the ball's speed at ?=21.7?

I have also attached a JPEG Image of a diagram of this problem. Thanks for your help!

A ball with mass m = 1.72 kg is attached to a peg at point C using a length of massless string of L = 1.54 m. It is released from the top of a vertical circle (gravity p oints down on the page) with speed to = 4.01 m/s as shown in the figure. Defining the angle as shown, what is the ball's speed at = 21.7"? 17-1 5 pts 2o m/s (± 0.02 m/s)

Explanation / Answer

The total energy is the same at both points.
Total(top) = Total(21.7deg)
PE(top) + KE(top) = PE(21.7deg) + KE(21.7deg)

You want to know speed, so you're mainly interested in the KE at 21.7degre.
KE(21.7deg) = KE(top) + (PE(top) - PE(21.7deg))
KE(21.7deg) = KE(top) + dPE
KE(21.7deg) = KE(top) + m g dh
(1/2) m v(21.7deg)^2 = (1/2) m v(top)^2 + (m * g * (L-(L*sin(theta)))) [cancel 0.5 and m from all terms]
v(21.7deg)^2 = v(top)^2 + 2g * (L-(L*sin(theta))))

v(21.7deg)^2 = 4.01^2 + 2*9.8*1.54[1 - sin21.7] = 35.104

v(21.7deg) = 5.92 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.