- Messages
- 187
- Reaction score
- 191
- Points
- 53
For Q8, regarding the ball. From X to Y, the ball accelerates uniformly till it reaches point Y, you could say that the weight of the ball is what's making it accelerate. When it passes Y, the ball is now on a horizontal surface, since weight acts vertically, the ball wont accelerate horizontally, so the graph is a straight line.
Now the important thing here is when the ball collides with the wall. Since it collides inelastically, kinetic energy is not conserved completely, this will affect the speed and make the ball travel slowly. They mention in the question, that after the collision the ball comes to rest momentarily somewhere on XY. Since the ball has to reach XY again, and this time with a lower speed, it's obviously going to take longer. Graphs B and D both indicate that it takes the same amount of time, which is not true, since to cover the same distance at a slower speed, will take a lot more time. This leaves us with C and A.
The difference in the two graphs is the steepness of the ends of the graphs. A steeper gradient means the acceleration is greater. If the ball is going to be approaching XY and come to rest, how can the acceleration to roll up be greater than when it was rolling down? This immediately eliminates C, and your answer is A.
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For Q14,
-You're told that the mass of the ruler is 100g, this will act at the halfway point of the ruler since it is a uniform ruler. So 100g acts at 50cm. Your pivot is at the 40cm mark.
That means that 100g acts downwards, 10 cm from the pivot.
-Next you're told that a mass of 20g acts around the pulley. This force is acting up since the string is pulling ruler up, as the weight of the mass acts down. This acts 60cm from the pivot, and acts upwards.
- The next and probably most important part of the question is them asking you where to " suspend " a mass of 50g to " balance " the rule. If the mass is to be suspended from the ruler it is to act downwards. Now the question is do we put it to the right or left of the pivot. To figure that out, we first check what the resultant moment is and in which direction.
That is ( 60 cm * 20g ) - ( 10 cm * 100g ) = 11760 - 9800 = 1960 Nm upwards.
Since the resultant moment is upwards, that means suspending the weight to the left of the pivot would be pointless. This would just make the ruler turn even more in the anti-clockwise direction. So this alone lets us know that the weight is to be placed to the right of the pivot, if we are to balance it.
Now you form your equations, keeping in mind that for the ruler to be in equilibrium, the resultant moment must equal zero.
Moments about Pivot: (100g x 10cm) + ( 50g x ycm ) - (20g x 60cm) = 0
This gives us: 9800 + 490y - 11760 = 0
490y = 1960 Ncm
y = 1960/490 = 4 cm
We now have our distance from the pivot, and since we know that the weight is to be suspended to the right, we add this distance to the position of the pivot.
40 cm + 4 cm = 44 cm, and thus your answer is C.
Hope that helps.
