Question

Two balls at same temperature collide. What is conserved (A) Temperature (B) velocity (C) kinetic energy (D) momentum

Short answer

In the collision of two balls at the same temperature, the conserved quantity is (D) momentum. Temperature, velocity, and kinetic energy are not conserved during the collision due to factors such as not relating to collision properties, the change in velocity due to forces, and insufficient information about the collision type. Momentum is conserved in both elastic and inelastic collisions, making it the correct answer.

Step-by-step solution

Analyze option A: Temperature

Temperature is a measure of the average kinetic energy of the particles in a system. While the two balls are at the same temperature, it does not imply that temperature is conserved during the collision, as temperature is not a property that relates to the dynamics of collisions. Therefore, option (A) is not correct.

Analyze option B: Velocity

Velocity depends on the mass and resulting forces during the collision. The velocity of each ball might change during the collision due to the applied forces between the balls. Also, the velocity of an individual object is not necessarily conserved in collisions. As such, option (B) is not conserved.

Analyze option C: Kinetic energy

Kinetic energy is given by the formula \(KE = \frac{1}{2}mv^2\), where m is the mass of the object and v is its velocity. In a perfectly elastic collision, the total kinetic energy of the system is conserved. However, in an inelastic collision, some kinetic energy is lost due to deformation and other factors. This exercise does not provide enough information to conclude which type of collision is taking place, and therefore, we cannot assume kinetic energy is conserved. So, option (C) is not correct.

Analyze option D: Momentum

Momentum is given by the formula \(p = mv\), where m is the mass of the object and v is its velocity. In all types of collisions (both elastic and inelastic), the total momentum of the system is always conserved. This property is known as the conservation of momentum. Given this information and ruling out the other options, option (D) is the correct answer. Hence, the conserved quantity in this collision is momentum.

Key concepts

Elastic and Inelastic Collisions

When objects collide, they can do so either elastically or inelastically. This distinction is all about how kinetic energy behaves during the collision. In an **elastic collision**, both momentum and kinetic energy are conserved. The colliding objects bounce off each other without any loss of kinetic energy.
This makes elastic collisions somewhat ideal, mostly occurring between atoms or in theoretical situations involving perfectly hard, non-deformable bodies.

However, **inelastic collisions** are much more common in daily life. During these collisions, momentum is still conserved, but some kinetic energy is transformed into other forms such as heat, sound, or deformation. In extreme cases of inelastic collisions, like car crashes, objects stick together after colliding.

• Elastic Collision: Both momentum and kinetic energy conserved.
• Inelastic Collision: Momentum conserved, kinetic energy is not.

The exercise above didn't specify the type of collision, which is crucial when considering conservation of kinetic energy. Hence, without this information, we can't assume kinetic energy conservation; however, we can confidently state that momentum conservation applies to both collision types.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion. It is given by the formula: \[KE = \frac{1}{2}mv^2\]where \(m\) represents mass and \(v\) is velocity. This type of energy depends heavily on an object's speed as velocity is squared, meaning even small increases in speed can significantly boost kinetic energy.

During collisions, the transfer of kinetic energy is often the focus. In elastic collisions, kinetic energy before and after the collision remains the same for the entire system. However, for **inelastic collisions**, a portion of this energy results in deformation or is dissipated as heat or sound. Consequently, collisions require us to analyze where energy goes and in what form.

• High velocities substantially increase kinetic energy.
• Conservation of kinetic energy only in elastic collisions.

Understanding kinetic energy allows us to predict how object behaviors change during collisions, which is often observed as an object slowing down after an inelastic collision or maintaining its speed in an elastic one.

Conservation Laws in Physics

Conservation laws play a critical role in understanding the mechanics of collisions and broader physics phenomena. Two primary principles often encountered are the conservation of momentum and the conservation of energy. These laws state that in a closed system, these quantities remain constant unless acted upon by external forces.

The **Conservation of Momentum** states that the total momentum of a system remains unchanged before and after a collision. This principle is universal for both elastic and inelastic collisions.
This means that while individual object velocities can change, the total system's momentum remains the same as long as no external forces intervene.

• Momentum before = Momentum after collision
• No external forces = Momentum conserved

On the other hand, the **Conservation of Energy** applies differently. While total energy is always conserved in a closed system, kinetic energy conservation holds true only for elastic collisions.
In inelastic collisions, energy is typically redistributed into other forms such as heat or potential energy.

• Kinetic energy conserved in elastic collisions.
• Energy conservation applies to overall system energy, but not in kinetic form for inelastic collisions.

Grasping these conservation principles helps in predicting outcomes of various physical phenomena, making them fundamental tools in analyzing any physics problem.