Former TAs Betsy and Patrick go into business together with a ride they invented

Question

Former TAs Betsy and Patrick go into business together with a ride they invented many years ago - the horizontal yo-yo. This ride consists of one person riding a frictionless cart while the other gives a push so that cart and rider pass under a bungee cord hanging from the ceiling. The rider grabs onto the bungee cord and hangs on for dear life.

Location A: point directly under the unstretched cord
Location B: point where cart has traveled as far as it can to the right
Velocity at point A: 8 ft/s to the right
Combined cart and rider weight: 167 lb
Bungee cord: k=14 lb/ft, 8.3 ft (unstretched length)
Positive directions: right and up

A: 0 ft/s
C: 0.000 ft/s

A. Cart at B:
What is the horizontal velocity of the cart?
(include units with answer)

A: 0 ft/s
C: 0.000 ft/s

Hi # tries: 1 B. Cart at B:
How far is the cord stretched from its neutral position?
(include units with answer)

C. Cart at B:
What is the distance that the cart traveled from A to B?
(include units with answer) D. Cart at B:
What is the vertical force of the floor on the cart?
(include units with answer) E. Cart at B:
What is the horizontal acceleration of the cart?
(include units with answer) F. Cart at A going to the left:
What is the horizontal velocity of the cart?
(include units with answer)

G. Cart at A going to the left:
What is the horizontal acceleration of the cart?
(include units with answer)

Explanation / Answer

B) k*x*x/2 = m*v*v/2 => x2 = 167*8*8/14 => x = 27.63ft Answer

C) distance2 = 35.93*35.93 - 8.3*8.3 => distance = 35ft

D) Vertical force = mg - kx*8.3/35.93 = 167*32.185 - 14*27.63*8.3/35.93 = 5285.53 pdl Answer

E) horizontal accleration =  kx*cos/m = 14*27.63*0.860/167 = 2 ft/sec2

F) 8 ft/s

G) zero ft/sec2

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