Question

A constant force applied to object A causes it to accelerate at 6 m/s2. The same force applied to object B causes an acceleration of 3 m/s2. Applied to object C, it causes an acceleration of 8 m/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) $m_A:m_B=1:2$

Explanation:

Newton's second law:

The acceleration of an object is directly proportional to the net external force applied, and it is indirectly proportional to its mass.

$\boxed{acceleration\ (a)=\frac{net\ force\ (F)}{mass\ (m)} }$

Therefore $\boxed{F=m\cdot a}$

Since $\bf F_A=F_B=F_C$, then $\bf m_A\cdot a_A=m_B\cdot a_B=m_C\cdot a_C$.

Therefore the greater the mass, the smaller the acceleration, which means the largest mass will have the smallest acceleration, while the smallest mass will have the biggest acceleration (providing they all have the same force).

Given:

$a_A=6\ m/s^2$

$a_B=3\ m/s^2$

$a_C=8\ m/s^2$

A)

Since object B has the smallest acceleration, then object B has the largest mass.

B)

Since object C has the largest acceleration, then object C has the smallest mass.

C)

$m_A\cdot a_A=m_A\cdot a_B$

$m_A:m_B=a_B:a_a$

$m_A:m_B=3:6$

$\bf m_A:m_B=1:2$