Question 1 :
(a). Two snooker balls, each of mass m, move freely on a frictionless, horizontal surface,
as shown in Figure Q1(a). Ball A is moving at a speed v0 = 10 m/s when it hits ball B
which is at rest and the impact causes ball B to break into two parts, each of mass m/2.
One of the parts reaches Point C about 0.07 s after the collision and the other part
reaches Point D about 0.09 s after the collision.
(i)
Determine the velocity of ball A after the collision.
(10 marks)
(ii)
Determine the angle θ and the velocities of the two parts after the collision.
(8 marks)
(iii) From your working in Q1(a)(i), explain with calculations and reasoning how the
velocity of ball A could move forward after the collision. (12 marks)
Figure Q1(a)
(b). You are required to design a roller coaster with the profile shown in Figure Q1(b).
An electric motor will pull the coaster to the top of the first hill. After the coaster has
been pulled to the top, no more external work will be added to it. Hint: the amount of
energy the coaster has to complete its journey on the track depends on the potential
energy on the first hill. This will give you the relationship between the height of this hill
and the speed of the coaster.
The shape of the first hill will determine if the coaster will safely travel on the track and
speed of the coaster. Hint: you can imagine the coaster as a particle that moves in space
along the track in a projectile motion.
The coaster exit through a second hill to maintain feeling of speed and thrill in the ride.
The second hill is also to maintain the speed to the next stage of the ride. Hint: the safety
of travel on the track depends on the speed you are travelling and is related to the hill
you are coming from.
Instead of adding a loop to your coaster, the coaster is allowed to gradually cruise to a
stop. Assume is a flat path.
(a)
(b)
(c)
(d)
Figure Q1(a) Profile of roller coaster: (a) The height of first hill height 20m, (b) Shape
of the first hill and radius at the bottom ρ = 60 m, (c) The exit path height 5m, and
(d) The loop to end the ride is a level ground, ignore the small height.
Assuming a total mass of 1000kg, explain with calculations how would you design the
roller coaster from start till the end of coaster ride:
(i)
the power of the electric motor to pull the coaster up the first hill.
(5 marks)
(ii)
the force at the bottom of the first hill to make sure it is strong enough to support
the coaster.
(5 marks)
(iii)
the radius of the exit hill and stopping distance of the coaster at the end of the
flat path, assuming a braking force 1500N is applied.
(5 marks)
(c). In the figures shown Figure Q1(c)(i), describe if the energy is conserved in each of
the activity described in the figure. Support your description with appropriate equations.
Figure Q1(c)-(a) A car is driven down a slope.
Figure Q1(c)-(b) A roller coaster
moving along smooth track.
Figure Q1(c)-(c) A bungee jumping from a tower.
Figure Q1(c)
(15 marks)