Roller Coaster In Fig. 10-28, a frictionless roller coaster of mass m = 517 kg t

Question

Roller Coaster In Fig. 10-28, a frictionless roller coaster of mass m = 517 kg tops the first hill with speed v1 = 5.9 m/s. Assume that the first hill is h = 51 m tall.

Figure 10-28
(a) How much work does the gravitational force do on it from the initial point to point A?
J
(b) How much work does the gravitational force do on it from the initial point to point B?
J
(c) How much work does the gravitational force do on it from the initial point to point C?
J

(d) If the gravitational potential energy of the coaster-Earth system is taken to be zero at point C, what is its value when the coaster is at point B?
J
(e) If the gravitational potential energy of the coaster-Earth system is taken to be zero at point C, what is its value when the coaster is at point A?
J
(f) If mass m were doubled, would the change in the gravitational potential energy of the system between points A and B increase, decrease, or remain same?
increase
remain same
decrease


DIAGRAM

http://img850.imageshack.us/i/diagr.gif/

Explanation / Answer

a. since particle returns to its orifginal height , so work done by gravity = 0 ;

W = 0 ;

b .

W = mg ( h - h/2 ) ;

W = mgh / 2 ;

c .

W = mg ( h - 0 ) ;

W = mgh ;

d .

PE = 0 at c , so it corresponds to x = 0 ;

B s coordinate = h / 2 ;

so U = mg ( h / 2 ) = mgh / 2 ;

e .

height above C = h ;

so U = mg h = mgh ;

f . if mass is doubled ,

U = 2mg h ,

U = 2mg ( h - h/2 )

U = mg h , so it has doubled as copared to mg ( h - h / 2 ) = mgh /2 ;

hence

it increses

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