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Q. 6

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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

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?

(a) B has the largest mass.

(b) C has the smallest mass.

(c)

See the step by step solution

Step by Step Solution

Part (a) : Step 1 : Given Information

Given :

A accelerates at :

B accelerates at :

C accelerates at :

Part (a) : Step 2 : Simplification

(a) When we apply a force to an object, it causes the thing to accelerate. According to Newton's rule, acceleration is inversely proportional to the mass of the object whereas it is directly proportional to the applied force , which is provided by : (1)

The mass of the item is , and the acceleration is The mass is inversely proportional to the acceleration, as given by equation (1).

As a result, the mass with the greatest mass will experience the least acceleration. Object B has the least acceleration, with , and thus the most mass, based on the supplied data.

As a result, B has the biggest mass.

Part (b) : Step 1 : Given Information

Given :

A accelerates at :

B accelerates at :

C accelerates at :

Part (b) : Step 2 : Simplification

(b) Object C accelerates faster than object A. Because, as we saw in paragraph (a), mass is inversely proportional to acceleration, the object with the greatest acceleration, in this case C, will have the smallest mass. As a result, C has the smallest mass.

Part (c) : Step 1 : Given Information

Given :

A accelerates at :

B accelerates at :

C accelerates at :

Part (c) : Step 2 : Simplification

(c) The acceleration is inversely proportional to the mass of the object, according to equation (1) in part (a).

We can get an equation for the two objects A and B when the force is constant as next (2)

from the relationship between a and m.

To calculate the ratio , we plug the values for and into equation (2) :

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