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Q.6b.

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 127

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Short Answer

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

The number of rubber bands required is 3 .

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Step by Step Solution

Step.1

The force can be expressed in terms of acceleration and the mass of the object as follows:

Step.2

Let us consider the number of rubber bands used to accelerate the object be and the force exerted by each rubber band on the object be .

Now, the total force exerted by the rubber bands is expressed as follows:

The net force on the object due to two rubber bands is,

Since, the two rubber bands causing the object of mass to accelerate at a rate of , replace the force with ma.

Rearrange the above equation for .

Express the acceleration of the new object with mass as follows:

Substitute 3a for for , and nF for .

Now, replace with and solve for .

Therefore, the number of rubber bands required is 3.

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