In the figure, a frictionless roller coaster of mass 1000 kg tops the first hill
ID: 1387703 • Letter: I
Question
In the figure, a frictionless roller coaster of mass 1000 kg tops the first hill at height, h = 50 m with speed 5.35 m/s.
a. How much work does its weight do on it from that point to point A?
b. How much work does its weight do on it from that point to point B?
c. How much work does its weight do on it from that point to point C?
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?
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?
Explanation / Answer
Given Data
mass m = 1000 kg
speed v0 = 5.35 m/s
height h = 50 m.
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Force of gravity on the car using the equation F = m*a
where a is equal to accelerationdue to gravity = 9.8 m/s^2
F = 1000*9.8 = 9800 N
a) Work is equal to the force applied to the object multiplied by the displacement of the object.
Since we are finding the workdone by gravitational force, we only consider the displacement of the car in the vertical direction.
The vertical displacement from the initial point to point A is zero, so the work done by the gravitational force is 0 J W = F*d = 9800*0 = 0 J --> Answer
b) From the initial point to point B, the vertical displacement is (h/2) (i.e 50/2)
W = F*d
= 9800*(50/2)
= 245000 J --> Answer
c) The vertical displacement from the initial point to point C is (h) (i.e 50)
W = F*d
= 9800*(50)
= 490000 J --> Answer
d) Since the displacement from point C to point B is (h/2), the work done is the same as part b.
The only difference is that W = -245000 J --> Answer
/*because the displacement is in the opposite direction of the gravitational force*/
e) Since the displacement from point C to point A is (h), the work done is the same as part c.
The only difference is that W= - 490000 J --> Answer
/*because the displacement is in the opposite direction of the gravitational force*/
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