Question

Two rubber bands cause an object to accelerate with acceleration a. How many rubber bands are needed to cause an object with half the mass to accelerate three times as quickly?

Answer 1

Answer:

3

Explanation:

We would use a rather simple analogy here. That of the relationship between force and mass. Remember the formula of Force is mass times acceleration, so

F = m * a

So 0.5m * 3a = 1.5 F

In words, the relationship above means that, if two rubber bands are able to produce a force F in parallel, then they will require 1.5 * 2 = 3 rubber bands arranged in parallel to be able to produce force a force of 1.5 F

Answer 2

The number of rubber bands that will cause an object with half the mass to accelerate three times as quickly is 3.

The given parameters;

• number of rubber band = 2
• acceleration = a

Let the mass of the object = m

The force applied to the object by the two rubber bands;

F = ma

2 = ma

When the mass of the object is halved, the number of rubber bands required is calculated as;

$\frac{2}{ma} = \frac{n}{m/2 \times 3a} \\\\\frac{2}{ma} = \frac{2n}{3ma} \\\\6ma = ma(2n)\\\\6 = 2n\\\\n = 3$

Thus, the number of rubber bands that will cause an object with half the mass to accelerate three times as quickly is 3.

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