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Chapter 4: Problem 9

An object is observed to be moving at constant speed along a line. Can you conclude that no forces are acting on it? Explain. [Based on a problem by Serway and Faughn.]

Short Answer

Expert verified
Forces may be acting, but they are balanced, resulting in zero net force and constant speed.

Step by step solution

01

Understanding Newton's First Law

Newton's First Law of Motion states that an object will remain at rest or move at a constant velocity unless acted upon by a net external force. This implies that if the object is moving at a constant speed, the net force acting on it must be zero.
02

Considering Forces and Net Force

Even though the object is moving at a constant speed, it does not imply there are no forces acting on it. For example, frictional forces may act against the movement; however, these might be balanced by other forces, like a push or pull of equal magnitude, resulting in a net force of zero.
03

Concluding Observation

Since the net force is zero due to balanced forces, the object continues at a constant speed. Therefore, we cannot conclude that no forces are acting on it, only that the forces are balanced.

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Key Concepts

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

Constant Speed
When we say an object is moving at a constant speed, it means the speed鈥攖he rate at which it covers distance鈥攄oesn't change over time. This is different from constant velocity, which also requires the direction to remain unchanged. Constant speed refers only to the magnitude of velocity staying the same.

To picture this, imagine a toy car rolling along a straight track. If the car moves from one end of the track to the other in exactly the same amount of time for each journey, that's constant speed. This happens because any forces like friction or air resistance are either minimal or effectively neutralized by other forces pushing the car. As such, the movement is smooth and unwavering.

Some key points to remember about constant speed:
  • Speed is the same at every point in time.
  • There are no accelerations (speeding up or slowing down).
  • It shows stability of motion in terms of speed.
Net Force
The concept of net force is crucial in understanding how objects move or stay at rest. It is the sum of all the forces acting on an object. So, if you imagine pushing a book across a table, the forces at play include your push, friction opposing the motion, and perhaps others like air resistance.

But what happens when these forces add up? This is where net force comes in. If all the forces cancel each other out, the net force is zero. According to Newton's First Law, this would mean the object will maintain its current state of motion. It will either stay still or keep moving at constant speed.

In summary:
  • Net force is the vector sum of all forces acting on an object.
  • If net force equals zero, the object's velocity won't change.
  • Zero net force means no acceleration; the object either stays at rest or moves with constant speed.
Balanced Forces
Balanced forces occur when all the forces acting on an object perfectly offset one another. This results in a net force of zero, which underlies objects maintaining constant speeds or remaining at rest.

Consider a book on a table. The gravitational force pulling it down is balanced by the table pushing it up. Neither force is stronger, so the book doesn't move. The same applies to an object moving at constant speed. If it's not accelerating, whether speeding up or slowing down, the forces must be balanced.

Here's what you need to know about balanced forces:
  • Forces are equal in size but opposite in direction.
  • The object does not change its state of motion.
  • This condition of balanced forces explains why an object can move at constant speed even when forces are acting on it.

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Most popular questions from this chapter

A dinosaur fossil is slowly moving down the slope of a glacier under the influence of wind, rain and gravity. At the same time, the glacier is moving relative to the continent underneath. The dashed lines represent the directions but not the magnitudes of the velocities. Pick a scale, and use graphical addition of vectors to find the magnitude and the direction of the fossil's velocity relative to the continent. You will need a ruler and protractor. (answer check available at lightandmatter.com)

A uranium atom deep in the earth spits out an alpha particle. An alpha particle is a fragment of an atom. This alpha particle has initial speed \(v\), and travels a distance \(d\) before stopping in the earth. (a) Find the force, \(F\), from the dirt that stopped the particle, in terms of \(v, d\), and its mass, \(m\). Don't plug in any numbers yet. Assume that the force was constant.(answer check available at lightandmatter.com) (b) Show that your answer has the right units. (c) Discuss how your answer to part a depends on all three variables, and show that it makes sense. That is, for each variable, discuss what would happen to the result if you changed it while keeping the other two variables constant. Would a bigger value give a smaller result, or a bigger result? Once you've figured out this mathematical relationship, show that it makes sense physically. (d) Evaluate your result for \(m=6.7 \times 10^{-27}\) kg, \(v=2.0 \times 10^{4} \mathrm{~km} / \mathrm{s}\), and \(d=0.71 \mathrm{~mm}\).(answer check available at lightandmatter.com)

While escaping from the palace of the evil Martian emperor, Sally Spacehound jumps from a tower of height \(h\) down to the ground. Ordinarily the fall would be fatal, but she fires her blaster rifle straight down, producing an upward force of magnitude \(F_{B}\). This force is insufficient to levitate her, but it does cancel out some of the force of gravity. During the time \(t\) that she is falling, Sally is unfortunately exposed to fire from the emperor's minions, and can't dodge their shots. Let \(m\) be her mass, and \(g\) the strength of gravity on Mars. (a) Find the time \(t\) in terms of the other variables. (b) Check the units of your answer to part a. (c) For sufficiently large values of \(F_{B}\), your answer to part a becomes nonsense - - explain what's going on.(answer check available at lightandmatter.com)

A gun is aimed horizontally to the west. The gun is fired, and the bullet leaves the muzzle at \(t=0\). The bullet's position vector as a function of time is \(\mathbf{r}=b \hat{\mathbf{x}}+c t \hat{\mathbf{y}}+d t^{2} \hat{\mathbf{z}}\), where \(b, c\), and \(d\) are positive constants. (a) What units would \(b, c\), and \(d\) need to have for the equation to make sense? (b) Find the bullet's velocity and acceleration as functions of time. (c) Give physical interpretations of \(b, c, d, \hat{\mathbf{x}}, \hat{\mathbf{y}}\), and \(\hat{\mathbf{z}}\).

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