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Chapter 4: Problem 4

Impulse indicates: (a) the momentum generated in the direction of force (b) the combined effect of mass and velocity (c) the main characteristics of particle nature (d) both (b) and (c) are correct

Short Answer

Expert verified
The correct answer is (a) the momentum generated in the direction of force.

Step by step solution

01

Definition of Impulse

Impulse is defined as the change in momentum of an object when a force is applied over a time interval. Mathematically, impulse can be expressed as \( J = F \times \Delta t \) where \( F \) is the force applied and \( \Delta t \) is the time period for which the force is applied.
02

Exploring Momentum

Momentum is the product of an object's mass and its velocity, expressed as \( p = m \times v \). It is a vector quantity, meaning it has both magnitude and direction. Impulse directly affects an object's momentum by changing it.
03

Analyzing the Options

Given the definition of impulse, we can conclude that option (a), "the momentum generated in the direction of force," is closely related to impulse. It implies the change in momentum in the direction of the applied force.
04

Reviewing Other Options

Option (b) describes momentum itself, not impulse. Option (c) is unrelated to impulse as it describes particle characteristics, which are not directly related to impulse. Therefore, option (d) is incorrect since both (b) and (c) are not valid when combined with impulse.
05

Final Answer Determination

Based on the analyzed information, the option that correctly describes the concept of impulse is (a) because impulse specifically relates to how momentum changes in the direction of the applied force.

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Key Concepts

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

Momentum
Momentum is a fundamental concept in physics. It represents the quantity of motion an object possesses. Simply put, momentum is the product of an object's mass and its velocity, given by the formula \( p = m \times v \). Both mass and velocity are crucial to determining how much momentum an object has. Because momentum is a vector quantity, it has both magnitude and direction.
Understanding momentum helps explain how objects move and interact. For instance, when a car moves east at a certain speed, its momentum will point east.
Key points about momentum are:
  • It depends on both mass and velocity.
  • It is vectorial; direction matters.
  • Conservation of momentum plays a critical role in understanding collisions.
Force and Time Interval
The relationship between force, time interval, and motion is essential in physics. When a force acts on an object over a period, it changes the object's momentum. This interaction is precisely what impulse describes. The formula for impulse, \( J = F \times \Delta t \), tells us how force and time duration combine to affect an object's motion.
Let's break down the components:
  • Force (F): The external influence that can change the motion of an object. Larger forces lead to greater changes in motion.
  • Time Interval (\(\Delta t\)): The period over which the force is applied. The longer the force acts, the more significant the change in motion.
These elements together show that both the strength and the application duration of a force determine how much an object's motion changes.
Change in Momentum
Change in momentum, often experienced as impulse, is a pivotal concept in dynamics. Impulse refers to how an object's momentum is altered when a force is applied over a short time period. This change can be calculated using the formula \( \Delta p = J = F \times \Delta t \).
Here's how change in momentum works:
  • A force acting on an object influences its velocity over time, thereby changing its momentum.
  • This change is vital in understanding phenomena like collisions, which involve rapid momentum alterations.
  • Change in momentum allows us to predict and analyze how objects will behave after being subjected to force.
In practical terms, whenever you see a sudden or gradual change in how fast something moves, you're witnessing a change in momentum.

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Most popular questions from this chapter

Two blocks of masses \(M=3 \mathrm{~kg}\) and \(m=2 \mathrm{~kg}\) are in contact on a horizontal table. A constant horizontal force \(F=5 \mathrm{~N}\) is applied to block \(M\) as shown. There is a constant frictional force of \(2 \mathrm{~N}\) between the table and the block \(m\) but no frictional force between the table and the first block \(M\), then acceleration of the two blocks is: (a) \(0.4 \mathrm{~ms}^{-2}\) (b) \(0.6 \mathrm{~ms}^{-2}\) (c) \(0.8 \mathrm{~ms}^{-2}\) (d) \(1 \mathrm{~ms}^{-2}\)

A body is moving down a long inclined plane of slope 37 \(^{\circ}\). The coefficient of friction between the body and plane varies as \(\mu=0.3 x\), where \(x\) is distance travelled down the plane. The body will have maximum speed. \(\left(\sin 37^{\circ}=\frac{3}{5}\right.\) and \(\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) (a) at \(x=1.16 \mathrm{~m}\) (b) at \(x=2 \mathrm{~m}\) (c) at bottom of plane (d) at \(x=2.5 \mathrm{~m}\)

A man is pulling a rope attached to a block on a smooth horizontal table. The tension in the rope will be the same at all points: (a) if and only if the rope is not accelerated (b) if and only if the rope is massless (c) if either the rope is not accelerated or is massless (d) always

A weight \(W\) is suspended from the midpoint of a rope, whose ends are at the same level. In order to make the rope perfectly horizontal, the force applied to each of its ends must be : (a) less than \(W\) (b) equal to \(W\) (c) equal to \(2 \mathrm{~W}\) (d) infinitely large

A particle of mass \(m\) moves on the \(x\) -axis as follows. It starts from rest at \(t=0\) from the point \(x=0\), and comes to rest at \(t=1\) at the point \(x=1\). No other information is available about its motion at intermediate time \((04\) at point or some points in its path (d) both (a) and (c) are correct
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