Question

Can a body have energy without having momentum? Explain.

Answer 1

Hint:We are going to use the concept of energy and momentum act on an object.An object's momentum is a virtue of its mass. It is defined as the mass and velocity product. It is the quantity of a vector.

Complete step by step solution:
The momentum of a moving object can be mathematically expressed as:
\[p = mv\]
Where,
\[p\] indicates the momentum of the moving body.
\[m\] indicates the mass of the object measured using \[kg\].
\[v\] indicates the velocity of an object measured using \[m/s\].
The SI unit of momentum is \[kg - m/s\] .
If the body is at rest in the gravity field, the velocity is zero so the body doesn't travel, so the speed is zero, but the body also has potential energy.
\[U = mgh\] (where, \[m\]=mass of the body)
But momentum is not possible without energy, since a body has momentum, which ensures that it travels at a certain velocity. There is kinetic energy in any force that travels with velocity.For example, a bucket of water of mass m at height h from the surface of the ground has Potential Energy \[U = mgh\]. But since it is stationary, it therefore has zero momentum. Therefore, the bucket has potential power, but zero is its momentum.

Hence, without momentum,it is possible for a body to provide energy.

Additional Information:
Potential Energy: This is the energy due to the location of an object relative to other objects.
The formula for potential energy depends on the force acting on the two objects. For the gravitational force the formula is:
\[W = m \times g \times h = mgh\]
Where, \[m\] is the mass of a body of an object
\[g\]is the acceleration due to gravity.
\[h\]is the height.
Kinetic Energy: An object's kinetic energy is the energy that it possesses because of its motion. Because of its movement or the energy acquired by an object from its state of rest to motion, it is the object.
Following is the formula of kinetic energy:
\[KE = \dfrac{1}{2}m{v^2}\]
Where ‘\[v\]’ is the velocity.

Note:We learned that kinetic energy is due to the motion of an object, where the position or state of an object is due to potential energy. When measuring the kinetic energy of an object, velocity is a significant aspect. Velocity has little to do with the potential energy of an object, however.