5. Charlie and Willy are in Mr. Wonka?s great glass elevator, which has mass M.

Question

5. Charlie and Willy are in Mr. Wonka?s great glass elevator, which has mass M. A chocolate candy bar, of mass m, is hanging by a string from the ceiling of the elevator. The elevator is being accelerated upward by a constant force F, such that F > (M + m)g. The candy bar is initially a distance s above the elevator floor. a) Show that the acceleration of the elevator is b) Show that the tension in the string is c) If the string suddenly breaks, show that the acceleration of the elevator immediately after is d) Show that the time it takes for the candy bar to hit the bottom of the elevator is

Explanation / Answer

(a)

according to newtons law of motion the net force is

Fnet = m a

Fnet = F - (M + m) g

m = (M + m)

then accleration will be

a = Fnet / m

= [F - (M + m) g] / (M + m)

(b)

the tension in the cable is

T = M (g + a)

where mass in our problem is (M + m)

a = [F - (M + m) g] / (M + m)

(c)

if the string suddenly breaks after that immediately lift moves up for a moment and again falls down

F = M(g + ae)

where ae is the acceleration of the elevator

(g + ae) = F / M

ae = (F / M) - g

(d)

for this we use

s = ut + (1 / 2) a t2

u = 0

a = F / M

s = (1 / 2) a t2

t2 = (2 M s / F)

t = sqrt(2 M s / F)

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