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Chapter 11: Problem 30

If you exert a net force of \(8 \mathrm{N}\) on a 2-kg object, what will its acceleration be?

Short Answer

Expert verified
The acceleration is \(4 \ \text{m/s}^2\).

Step by step solution

01

Identify the given values

First, identify and write down the given values. Here, the net force applied is given as \(F = 8 \ \text{N}\) and the mass of the object is \(m = 2 \ \text{kg}\).
02

Use Newton's Second Law

Newton's Second Law states that the acceleration \(a\) of an object is given by the formula \[a = \frac{F}{m}\text{,} \] where \(F\) is the net force and \(m\) is the mass of the object.
03

Plug in the values

Substitute the given values into the formula: \[a = \frac{8 \ \text{N}}{2 \ \text{kg}}\].
04

Calculate the acceleration

Perform the division to find the acceleration: \[a = \frac{8}{2} \ \text {m/s}^2 = 4 \ \text{m/s}^2.\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Net Force
Net force is the total force acting on an object when all individual forces are combined. It is important to think of net force as the cumulative effect of all forces. Consider an object being pushed from different directions. Each push or pull contributes to the net force. If you have a force of 10 N to the right and a force of 2 N to the left, the net force is 10 N - 2 N = 8 N to the right. This net value helps us predict the object's motion. Understanding net force is crucial because it directly influences acceleration, according to Newton's Second Law.
The Role of Mass
Mass is a measure of the amount of matter in an object. It is often confused with weight, which is the force exerted by gravity on that mass. Mass remains constant regardless of location, while weight can change with gravity. In the context of Newton's Second Law, mass acts as a resistance to acceleration. A greater mass requires a greater force to achieve the same acceleration. For example, accelerating a car requires much more force than accelerating a bicycle due to the car's larger mass. This concept is vital when calculating acceleration using the formula \(a = \frac{F}{m}\).
Acceleration Explained
Acceleration is the rate at which an object's velocity changes over time. It can be caused by changes in speed, direction, or both. According to Newton's Second Law, acceleration is produced when a net force acts on a mass. The relationship is given by the formula \(a = \frac{F}{m}\). This means that for a given force, the acceleration is inversely proportional to the mass. If the net force on an object is increased, the acceleration will increase if the mass is constant, and vice versa. Calculating acceleration is essential for understanding how quickly an object can change its motion under a given force.

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