A hollow ball of mass m is released from rest at a height h above the base of a

Question

A hollow ball of mass m is released from rest at a height h above the base of a loop-the-loop track, as shown in the figure. The loop has a radius R = 22.0 cm. Assume that the ball?s radius is much smaller than the loop?s, and that the ball rolls without slipping at all times. Use g = 10 m/s^2.

What is the minimum value of h (in centimeters) necessary for the ball to make it all the way around the loop without losing contact with the track? (cm)

Be sure to take into account the rotation energy of the ball.

A hollow ball of mass m is released from rest at a height h above the base of a loop-the-loop track, as shown in the figure. The loop has a radius R = 22.0 cm. Assume that the ball?s radius is much smaller than the loop?s, and that the ball rolls without slipping at all times. Use g = 10 m/s^2. What is the minimum value of h (in centimeters) necessary for the ball to make it all the way around the loop without losing contact with the track? (cm) Be sure to take into account the rotation energy of the ball.

Explanation / Answer

apply mgh = 0.5 mv^2 + mg H

here H = 2R

so mg + N = mv^2/R

mg = mv^2/R

mgh = 0.5 mgR    + 2 mgR

h = 1.5 R

h = 1.5* 22

h = 33 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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