physics Charlie and Willy are in Mr. Wonka\'s great glass elevator, which has ma

Question

physics

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. Show that the acceleration of the elevator is alpha = F - (M + m)g / M + m Show that the tension in the string is T = mF/M + m. If the string suddenly breaks, show that the acceleration of the elevator immediately after is alphae = F/M - g. Show that the time it takes for the candy bar to hit the bottom of the elevator is t = 2sM/F.

Explanation / Answer

a) sum forces for the elevator

F - (M + m) g = (M + m) a

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

b)

for just the mass

T - mg = ma

T - mg = m ( F - (M +m)g)/(M + m)
T = m ( F - (M +m)g)/(M + m) + mg

common denominator

T = (m F - M m g - m^2 g + m M g + m^2 g)/(m + M)

T = m F/( M + m)

c) just after it breaks no longer supporting mass m

so
F - Mg = M a

a = F/m - g

d) so for candy bar x = s - 1/2 g t^2

for elevator x = 1/2 a t^2 = 1/2 (F/m - g) t^2
s - 1/2 g t^2 = 1/2 F/m t^2 - 1/2 g t^2

s= 1/2 F/M t^2

t = sqrt( 2 s M/F)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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