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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

A \(2.50-\mathrm{kg}\) block is placed on a rough surface inclined at \(30^{\circ} .\) The block is propelled and launched at a speed of \(1.60 \mathrm{~m} / \mathrm{s}\) down the incline and comes to rest after sliding \(1.10 \mathrm{~m} .\) (a) Draw the free-body diagram of the block while it is sliding. Also indicate your coordinate system axes. (b) Starting with Newton's second law applied along both axes of your coordinate system, use your free- body diagram to generate two equations. (c) Solve these equations for the coefficient of kinetic friction between the block and the incline surface. [Hint: You will need to first determine the block's acceleration.]

A gun is fired and a \(50-\mathrm{g}\) bullet is accelerated to a muzzle speed of \(100 \mathrm{~m} / \mathrm{s}\). If the length of the gun barrel is \(0.90 \mathrm{~m}\), what is the magnitude of the accelerating force? (Assume the acceleration to be constant.)

A student is assigned the task of measuring the startup acceleration of a large RV (recreational vehicle) using an iron ball suspended from the ceiling by a long string. In accelerating from rest, the ball no longer hangs vertically, but at an angle to the vertical. (a) Is the angle of the ball forward or backward from the vertical? (b) If the string makes an angle of 3.0 degrees from the vertical, what is the initial acceleration of the RV?

IE oo A hockey puck with a weight of \(0.50 \mathrm{lb}\) is sliding freely across a section of very smooth (frictionless) horizontal ice. (a) When it is sliding freely, how does the upward force of the ice on the puck (the normal force) compare with the upward force when the puck is sitting permanently at rest: (1) The upward force is greater when the puck is sliding; (2) the upward force is less when it is sliding; (3) the upward force is the same in both situations? (b) Calculate the upward force on the puck in both situations.

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?
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