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 .
The force can be expressed in terms of acceleration and the mass of the object as follows:
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.
A constant force applied to A causes A to accelerate at . The same force applied to B causes an acceleration of . Applied to C, it causes an acceleration of .
a. Which object has the largest mass? Explain.
b. Which object has the smallest mass?
c. What is the ratio of the mass of A to the mass of B?
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