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Chapter 4: Problem 12

A 6.0 -N net force is applied to a 1.5 -kg mass. What is the object's acceleration?

Short Answer

Expert verified
The object's acceleration is 4.0 m/s虏.

Step by step solution

01

Identify the Formula

To find the acceleration of an object, we use Newton's second law of motion, which is expressed as \( F = ma \), where \( F \) is the net force applied to the object, \( m \) is the mass of the object, and \( a \) is the acceleration.
02

Substitute the Given Values

We are given that the net force \( F \) is 6.0 N and the mass \( m \) is 1.5 kg. We need to find the acceleration \( a \). Substitute the given values into the formula: \( 6.0 = 1.5 \, a \).
03

Solve for Acceleration

Rearrange the formula to solve for \( a \). Divide both sides of the equation by the mass \( m \): \( a = \frac{F}{m} = \frac{6.0}{1.5} \).
04

Calculate the Acceleration

Perform the division: \( a = \frac{6.0}{1.5} = 4.0 \). Thus, the acceleration \( a \) is 4.0 m/s^2.

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Key Concepts

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

Net Force
In physics, the concept of net force is fundamental to understanding how objects move and interact. Net force is the total force acting on an object. It is the vector sum of all the individual forces that are applied to the object.

Here are some key points about net force:
  • When all the forces acting on an object are added together, taking into account their directions, the result is called the net force.
  • If the net force is zero, the object remains at rest or moves at constant velocity. This is known as equilibrium.
  • If the net force is not zero, the object will accelerate in the direction of the net force. This means its motion will change, in either speed, direction, or both.
In our given exercise, a net force of 6.0 N is applied. This means that all the individual forces acting on the object combine to create a total force of 6.0 Newtons. Understanding net force is crucial for applying Newton's Second Law of Motion effectively.
Mass
Mass is a measure of the amount of matter in an object. It is a fundamental property that provides a quantitative measure of inertia. In simple terms, inertia is the resistance of an object to any change in its state of motion.

Some important aspects of mass include:
  • Mass is usually measured in kilograms (kg) in the metric system.
  • It is a scalar quantity, which means it has magnitude but no direction.
  • Mass is different from weight, which is the force exerted by gravity on that mass.
In the context of our exercise, we are working with a mass of 1.5 kg. This means our object has a certain resistance to changes in its motion, corresponding to this mass. The greater the mass of an object, the more force is required to change its motion. This concept is central to understanding how different factors influence acceleration as described by Newton's Second Law.
Acceleration
Acceleration is the rate of change of velocity of an object. It occurs when there is a change in speed, direction, or both. It is a vector quantity, meaning it has both magnitude and direction.

Key details about acceleration include:
  • In the metric system, acceleration is measured in meters per second squared (m/s虏).
  • According to Newton's Second Law of Motion, acceleration occurs in the direction of the net force applied on an object.
  • The formula for acceleration is given by the equation: \( a = \frac{F}{m} \), where \( F \) is the net force and \( m \) is the mass.
In the example problem, we calculated the acceleration by dividing the net force of 6.0 N by the mass of 1.5 kg, resulting in an acceleration of 4.0 m/s虏. This tells us the object speeds up by 4 meters per second every second when the force is applied.

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Most popular questions from this chapter

In an Olympic figure-skating event, a 65-kg male skater pushes a \(45-\mathrm{kg}\) female skater, causing her to accelerate at a rate of \(2.0 \mathrm{~m} / \mathrm{s}^{2}\). At what rate will the male skater accelerate? What is the direction of his acceleration?

One block (A, mass \(2.00 \mathrm{~kg}\) ) rests atop another (B, mass \(5.00 \mathrm{~kg}\) ) on a horizontal surface. The surface is a powered walkway accelerating to the right at \(2.50 \mathrm{~m} / \mathrm{s}^{2}\). \(\mathrm{B}\) does not slip on the walkway surface, nor does A slip on B's top surface. (a) Sketch the free-body diagram of each block. Use these to determine the force responsible for A's acceleration. Is it (1) the pull of the walkway, (2) the normal force on A by the top surface of \(B\), (3) the force of static friction on the bottom surface of \(\mathrm{B}\), or (4) the force of static friction acting on A due to the top surface of B? (b) Determine the forces of static friction on each block.

IE .?? Three horizontal forces (the only horizontal ones) act on a box sitting on a floor. One (call it \(F_{1}\) ) acts due east and has a magnitude of \(150 \mathrm{lb}\). A second force (call it \(F_{2}\) ) has an easterly component of \(30.0 \mathrm{lb}\) and a southerly component of \(40.0 \mathrm{lb}\). The box remains at rest. (Neglect friction.) (a) Sketch the two known forces on the box. In which quadrant is the unknown third force: (1) the first quadrant; (2) the second quadrant; (3) the third quadrant; or (4) the fourth quadrant? (b) Find the unknown third force in newtons and compare your answer to the sketched estimate.

The coefficients of static and kinetic friction between a \(50.0-\mathrm{kg}\) box and a horizontal surface are 0.500 and 0.400 respectively. (a) What is the acceleration of the object if a 250-N horizontal force is applied to the box? (b) What is the acceleration if the applied force is \(235 \mathrm{~N}\) ?

A book is sitting on a horizontal surface. (a) There is (are) (1) one, (2) two, or (3) three force(s) acting on the book. (b) Identify the reaction force to each force on the book.
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