In the figure, a small block of mass m = 0.034 kg can slide along the frictionle

Question

In the figure, a small block of mass m = 0.034 kg can slide along the frictionless loop-the-loop, with loop radius R = 18 cm. The block is released from rest at point P, at height h = 5R above the bottom of the loop. What are the magnitudes of (a) the horizontal component and (b) the vertical component of the net force acting on the block at point Q? (c) At what height h should the block be released from rest so that it is on the verge of losing contact with the track at the top of the loop? (On the verge of losing contact means that the normal force on the block from the track has just then become zero).

In the figure, a small block of mass m = 0.034 kg can slide along the frictionless loop-the-loop, with loop radius R = 18 cm. The block is released from rest at point P, at height h = 5R above the bottom of the loop. What are the magnitudes of (a) the horizontal component and (b) the vertical component of the net force acting on the block at point Q? (c) At what height h should the block be released from rest so that it is on the verge of losing contact with the track at the top of the loop? (On the verge of losing contact means that the normal force on the block from the track has just then become zero).

Explanation / Answer

  5R - 1R = 4R = 68cm = 0.68m = initial height

Ug at initial height = mgh = K at point P = mv^2

mgh = mv^2

gh = v^2

6.664m^2/s^2 = v^2

v at Q = 2.581m/s

Horizonal acceleration at p = v^2/r = (6.664m^2/s) / (0.17m) = 39.2m/s^2 toward the center

a) Centripetal force at Q = 0.049kg(39.2m/s^2) = 1.92N(left)
b) 0.049kg(9.8m/s^2) = 0.48N (down)

d)
(v^2 / r) = a = g = 9.8m/s^2

(9.8m/s^2)(r) = v^2

1.666m^2/s^2 = v^2

1.29m/s = v at top

K = 1/2mv^2 = 0.040817J

Ug = mgh = 0.040817J

0.040817J/(0.049)(9.8) = h

h = 0.085m = 0.5R from the top (which is 2R from the ground)

So the inital height would be 2.5R from the ground.

42.5cm from the ground would be the initial height to barely make it.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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