Question

What is the resulting acceleration of a 100-kg object if 1,000 N of force is applied to it and it is opposed by a force of kinetic friction equivalent to 100.0 N?

Answer 1

`9\; {\rm m\cdot s^(-2)}`.

Step-by-step explanation:

For an object of mass
`m`, acceleration would be proportional to the net force on this object:

`\displaystyle a = \frac{F_{\text{net}}}{m}`,

Where:

• 
  `F_{\text{net}}` is the net force on this object, and
• 
  `m` is the mass of this object.

Assume that aside from kinetic friction and the
`1000\; {\rm N}` external force, all other forces (for example, weight and normal force) are balanced. To find the acceleration of this object, start by deriving the net force. After that, divide net force by the mass of the object to find the acceleration on this object.

Under the assumptions, the only unbalanced forces on this object are:

• The external force of
  `1000\; {\rm N}`, and
• Kinetic friction of
  `(-100.0)\; {\rm N}` (negative because friction opposites motion and is in the opposite direction of the external force.)

The net force would be the vector sum of all unbalanced forces on this object:

`\begin{aligned} F_{\text{net}} &= (1000)\; {\rm N} + (-100.0)\; {\rm N} \\ &= 900.0\; {\rm N}\end{aligned}`.

Divide the net force on the object by mass to find acceleration:

`\begin{aligned}a &= \frac{F_{\text{net}}}{m} \\ &= \frac{900.0\; {\rm N}}{100\; {\rm kg}} = 9\; {\rm m\cdot s^(-2)}\end{aligned}`.