Q. 6

Expert-verifiedFound in: Page 127

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

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)

__Given__ :

A accelerates at :

B accelerates at :

C accelerates at :

(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.

__Given__ :

A accelerates at :

B accelerates at :

C accelerates at :

(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.

__Given__ :

A accelerates at :

B accelerates at :

C accelerates at :

(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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