4. A mini car of mass 42 g moves in a circular track shown in Figure 3. Assume t

Question

4. A mini car of mass 42 g moves in a circular track shown in Figure 3. Assume that friction
between the car wheels and the track is negligible.
(a) Draw free-body diagram for the car at A.(3 Points.)
(b) Find the normal force exerted by the track on the car at A. (4 Points.)
(c) Draw free-body diagram for the car at point B.(3 Points.)
(d) Find the normal force exerted by the track on the car at B. (4 Points.)
(e) What is the minimum speed required for the car in order to remain in contact with
the track at A? (3 Points.)
(f) Determine the normal force on the car at point C. (3 Points.)

m = 42g
r = 13 cm
Speed at A = 1.69 m/s
Speed at B = 2.81 m/s
Speed at C = 2.32 m/s


Note: the picture is a car going around a loop dee loop. Point A (where the car is at) is at the top, Point B is the bottom, and Point C is at 9 o'clock position.

Explanation / Answer

b) F= n+mg= mV2/r

ntop=mV2/r- mg = mg(v2/rg -1)

ntop= (0.042kg)(9.8m/s2)((1.69m/s)2/(0.13m)(9.8m/s2) -1)

   = 0.511N

d)

F= n-mg= mV2/r

nbot=mV2/r- mg = mg(v2/rg +1)

nbot= (0.042kg)(9.8m/s2)((2.81m/s)2/(0.13m)(9.8m/s2) -1)

   = 2.96N

e) n-mg =mv2/r

v = (r(n-mg)/m)

   = (0.13m)(0.511N - 0.4116N)/(0.042kg)

   = 0.55m/s

f)

F= nc+mg= mV2/r

nc=mV2/r- mg = mg(v2/rg -1)

nc= (0.042kg)(9.8m/s2)((2.32m/s)2/(0.13m)(9.8m/s2) -1)

   = 1.33N

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