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Chapter 2: Problem 3

A body moving towards a body of finite mass at rest collides with it. It is possible that (1) both bodies come to rest (2) both bodies move after collision (3) the moving body stops and the body at rest starts moving (4) the stationary body remains stationary and the moving body rebounds

Short Answer

Expert verified
Options 2, 3, and 4 are all possible scenarios in a collision.

Step by step solution

01

Understand the Collision Types

In physics, collisions can be broadly categorized into elastic and inelastic collisions. In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not.
02

Analyze Both Bodies Coming to Rest

If both bodies come to rest after the collision, it implies that both momentum and kinetic energy have not been conserved. This scenario is typically impossible unless an external force acts on the system.
03

Evaluate Both Bodies Moving After Collision

In many collision scenarios, both bodies move after collision, especially in elastic collisions, where momentum and kinetic energy allow for continuous motion. Thus, this scenario is plausible.
04

Consider Moving Body Stops, Stationary Body Moves

This scenario is described by inelastic collisions where all the momentum is transferred from one body to the other. It is possible and commonly observed when a moving body transfers its momentum to a resting body and itself stops.
05

Examine Stationary Body Remains, Moving Body Rebounds

In certain elastic collision situations, a moving body can rebound if the stationary body is very massive compared to the moving body. This can happen if the mass of the moving body is negligible compared to the stationary one.

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Key Concepts

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

Elastic Collision
An elastic collision is a type of collision where both momentum and kinetic energy are conserved. This means that after the collision, the total momentum and total kinetic energy of the system remain the same as they were before the collision.
This kind of collision is ideal and is often used as a theoretical model, since in the real world, some energy is usually lost as heat or sound.
  • In an elastic collision, both objects may move after the impact, depending on their masses and velocities.
  • It is also possible for one object to rebound if the other one is significantly more massive, thus maintaining the overall kinetic energy.
  • Since energy is conserved, the speed of the objects may change, but the total kinetic energy of the system does not.
Inelastic Collision
In an inelastic collision, only momentum is conserved, while kinetic energy is not.
This means some kinetic energy is lost, typically turned into other forms of energy like heat or sound.
  • In a perfectly inelastic collision, the two bodies stick together after the collision, resulting in the maximum possible loss of kinetic energy.
  • Such collisions are common in the real world, such as when cars collide and crumple together.
  • The outcome often involves changes in speed and direction depending on the mass and velocity of each object.
Momentum Conservation
In physics, momentum conservation is a fundamental principle stating that the total momentum of a closed system remains constant, provided no external forces are acting on it.
This principle holds true for both elastic and inelastic collisions.
  • Momentum is calculated as the product of an object's mass and velocity \( p = mv \).
  • In a collision scenario, the total momentum before the collision (sum of the momentum of all individual bodies) is equal to the total momentum after the collision.
  • This concept helps to predict the final velocities of objects after they collide.
Kinetic Energy Conservation
Kinetic energy conservation is a key concept in understanding elastic collisions, where kinetic energy is conserved before and after the collision.
This is crucial for predicting the outcomes of elastic collisions.
  • Kinetic energy is defined as \( KE = \frac{1}{2}mv^2 \).
  • In elastic collisions, the total kinetic energy before impact equals the total kinetic energy after impact.
  • The conservation of kinetic energy ensures that the objects involved in the collision retain their energy as motion rather than losing it to other forms like heat.

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Most popular questions from this chapter

A steel ball of mass \(2 \mathrm{~m}\) suffers one-dimensional elastic collision with a row of three steel balls, each of mass \(m\). If mass \(2 m\) has collided with velocity \(v\) and the three balls numbered \(1,2,3\) were initially at rest, then after the collision (1) balls 1,2 and 3 would start moving to the right, each \(_{w_{2}}\) velocity \(v / 3\) (2) balls 2 and 3 would start moving to the right, each \(w_{10}\) velocity \(v / 2\) (3) balls 2 and 3 would start moving to the right, each \(w_{2}\) velocity \(v\) (4) ball 1 and ball of mass \(2 m\) would remain at rest

A \(3000 \mathrm{~kg}\) space probe is moving in a gravity free space at a constant velocity of \(300 \mathrm{~m} / \mathrm{s}\). To change the direction of space probe, rockets have been fired in a direction perpendicular to the direction of initial motion of the space probe, the rocket firing exerts a thrust of \(4000 \mathrm{~N}\) for \(225 \mathrm{~s}\). The space probe will turn by an angle of (neglect the mass of the rockets fired) (1) \(30^{\circ}\) (2) \(60^{\circ}\) (3) \(45^{\circ}\) (4) \(37^{\circ}\)

A ball strikes a wall with a velocity \(\vec{u}\) at an angle \(\theta\) with the normal to the wall surface and rebounds from it at an angle \(\beta\) with the surface. Then (1) \((\theta+\beta)<90^{\circ}\), if the wall is smooth (2) if the wall is rough, coefficient of restitution \(=\tan \beta / \cos \theta\) (3) if the wall is rough, coefficient of restitution \(<\tan \beta / \cot \theta\) (4) none of the above

A body of mass \(3 \mathrm{~kg}\) collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body? (1) \(1 \mathrm{~kg}\) (2) \(1.5 \mathrm{~kg}\) (3) \(2 \mathrm{~kg}\) (4) \(5 \mathrm{~kg}\)

Two blocks \(A\) and \(B\) of masses \(m\) and \(2 m\), respectively, are connected with the help of a spring having spring constant, \(k\) as shown in figure. Initially, both the blocks are moving with same velocity \(v\) on a smooth horizontal plane with the spring in its natural length. During their course of motion, block \(B\) makes an inelastic collision with block \(C\) of mass \(m\) which is initially at rest. The coefficient of restitution for the collision is \(1 / 2 .\) The maximum compression in the spring is
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