2019 A/L Physics Past Paper · Question 35 (English Medium)

Answer: (4) Diagram (4)

What the question asks

We want:

How the string of the balloon leans in $t_1$, $t_2$ and $t_3$.

Then we pick the matching diagrams.

Relevant theory

Newton's first law states that a resultant force can change the state of motion of an object.

When a body is completely or partially immersed in a fluid at rest, it experiences an upthrust equal to the weight of the fluid displaced by the body.

The balloon has no mass.

So only two forces act on it: the push of the water and the pull of the string.

They are equal in size and opposite in direction.

So the string lies along the direction of the water's push.

Applying it to this question

In the figure the truck moves to the right.

The tank is full of water.

The balloon is tied to the bottom of the tank by a string.

On the graph the speed rises in $t_1$, stays flat in $t_2$ and falls in $t_3$.

The walls of the tank push the water along.

The water pushes the balloon.

The string holds the balloon to the bottom.

$t_1$: the truck speeds up. The acceleration $a$ points forward.

$t_2$: the speed does not change. So $a = 0$.

$t_3$: the truck slows down. The deceleration points backward.

Reasoning and calculation

To speed the water up, the pressure at its back must be higher.

So the pressure falls from back to front.

The balloon is lighter than water.

So the water pushes it to the low-pressure side.

That is the front, the way the truck speeds up.

The lean of the string is:

$$\tan\theta = \frac{a}{g}$$

$t_1$ (acceleration)

The truck speeds up to the right.

The pressure is higher at the back of the water.

So the balloon leans forward, to the right.

$t_2$ (constant velocity)

The speed does not change.

There is no sideways difference in pressure.

So the balloon stands straight up.

$t_3$ (deceleration)

The deceleration points backward.

So the balloon leans backward, to the left.

Reading the options

Only diagram (4) shows forward, then straight, then backward.

Why the other options fail

This option says: the balloon is straight up in all three.

But when the truck speeds up or slows down, the pressure at the back and at the front of the water is different. So the balloon must lean.

So it is wrong.

This option says: backward in $t_1$, straight in $t_2$, forward in $t_3$.

That is how a pendulum bob leans.

But a balloon is lighter than water. So it leans the other way.

This option says: the balloon leans backward in all three.

But in $t_2$ the speed does not change. So there is no push to the side, and the balloon stands straight.

This option says: the balloon leans forward in all three.

It leans forward only in $t_1$, when the truck speeds up. In $t_2$ the balloon is straight. In $t_3$ it leans backward.

Checks

Does it make sense?

Hold a helium balloon in a car.

When the car sets off, the balloon moves forward.

That is the same reason.

Take $a = 3\ \text{m s}^{-2}$.

$$\theta = \tan^{-1}(0.3) \approx 17°$$

Conclusion

Forward while speeding up.

Straight at a steady speed.

Backward while slowing down.

So the answer is diagram (4).

Thinking of the balloon as a pendulum, so that it leans backward when the truck speeds up.

A pendulum bob is denser than what is around it.

The balloon is lighter than what is around it.

So it leans the other way.