High School

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A 41 kg mass is pushed across a carpeted floor with a force of 196 N. There is a -32.0 N force due to friction. What is the acceleration of the mass?

[tex] a = [?] \, \text{m/s}^2 [/tex]

Answer :

We are given the following values:

- Mass: [tex]$m = 41\, \text{kg}$[/tex]
- Applied force: [tex]$F_{\text{applied}} = 196\, \text{N}$[/tex]
- Friction force: [tex]$F_{\text{friction}} = -32.0\, \text{N}$[/tex] (the negative sign indicates that friction opposes the motion)

Step 1: Determine the Net Force

The net force acting on the mass is the sum of the applied force and the friction force:

[tex]$$
F_{\text{net}} = F_{\text{applied}} + F_{\text{friction}} = 196\, \text{N} + (-32.0\, \text{N}) = 164\, \text{N}
$$[/tex]

Step 2: Apply Newton's Second Law

Newton's second law states that the net force acting on an object equals the mass of the object multiplied by its acceleration:

[tex]$$
F = m \cdot a
$$[/tex]

Solving for acceleration [tex]$a$[/tex], we have:

[tex]$$
a = \frac{F_{\text{net}}}{m}
$$[/tex]

Substitute the net force and the mass into the equation:

[tex]$$
a = \frac{164\, \text{N}}{41\, \text{kg}} = 4.0\, \text{m/s}^2
$$[/tex]

Final Answer:

The acceleration of the mass is

[tex]$$
a = 4.0\, \text{m/s}^2.
$$[/tex]

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