Question

If an object's velocity increases from 13.2 m/s to 15.1 m/s in 8.0 seconds and experiences a force of 21.0 N, what is the mass of the object?

Answer 1

Approximately
`88\; {\rm kg}`, assuming that the
`21.0\; {\rm N}` force is the only force on this object.

Step-by-step explanation:

In this question, the change in the velocity of the object, the duration of the motion, and the net force on the object are given. The mass of this object can be found in the following steps:

• Find the acceleration of the object.
• Divide the net force on the object by acceleration to find the mass of the object.

In this question, the velocity of this object has changed from
`u = 13.2\; {\rm m\cdot s^(-1)}` to
`v = 15.1\; {\rm m\cdot s^(-1)}` within a period of
`t = 8.0\; {\rm s}`. Additionally, it is given that the net force on the object is constant, such that acceleration (rate of change in velocity) would also be constant. Divide the change in velocity by the duration of the motion to find acceleration:

`\begin{aligned}a &= (v - u)/(t) \\ &= (15.1 - 13.2)/(8.0)\; {\rm m\cdot s^(-2)} \\ &\approx 0.238\; {\rm m\cdot s^(-2)}\end{aligned}`.

Divide the net force
`F_{\text{net}}` on this object by the acceleration to find the mass of this object:

`\begin{aligned}m &= \frac{F_{\text{net}}}{a} \\ &\approx \frac{21.0\; {\rm N}}{0.238\; {\rm m\cdot s^(-2)}} \\ &\approx 88\; {\rm kg}\end{aligned}`.

In other words, the mass of this object would be approximately
`88\; {\rm kg}`.