Question

A constant force applied to object A causes it to accelerate at 6m/s2 .The same force applied to object B causes an acceleration of 3m/s2 . Applied to object C, it causes an acceleration of 7m/s2 .
A) Which object has the largest mass?

B) Which object has the smallest mass?

C) What is the ratio of mass A to mass B?

Answer 1

Answer:

A) Object B

B) Object C

C) $\frac{m_A}{m_B} = \frac{7}{6}$

Explanation:

We should apply Newton's Second Law to each object to find their masses.

Object A:

$F = m_Aa_A = m_A(6)\\m_A = \frac{F}{6}$

Object B:

$F = m_Ba_B = m_B(3)\\m_B = \frac{F}{3}$

Object C:

$F = m_Ca_C = m_C(7)\\m_C = \frac{F}{7}$

A) According to above results, object B has the largest mass.

B) According to above results, object C has the smallest mass.

C) $\frac{m_A}{m_B} = \frac{F/6}{F/7} = \frac{7}{6}$

This question is a clear example of the definition of mass. According to above results; higher the mass, smaller the acceleration. This means that mass is resistance to acceleration.

Answer 2

Explanation:

Force, F = M * a

Where,

M = mass

a = acceleration

Object A

F = Ma * 6

= 6Ma

Object B

F = Mb * 3

= 3Mb

Object C

F = Mc * 7

= 7Mc

A.

Calculating their masses,

Object A

F/6 = Ma

Object B

F/3 = Mb

Object C

F/7 = Mc

Object B of mass, F/3 has the largest mass.

B.

Object C of mass, F/7 has the smallest mass.

C.

Mass of Object A : Mass of Object B

= F/6 : F/3

= 1 : 2