 # Momentum equation

3 problems and solutions about Momentum equation

1. If the object’s speed becomes 5 times its original speed, then the object’s momentum becomes ….. its original momentum.

Known:

Initial speed = v

Final speed = 5v

Mass = 1

Wanted: Momentum

Solution:

Momentum formula

p = m v = 1 (5) = 5

If the speed is 5 times the original and the mass is constant then the momentum is 5 times the original.

2. An object is thrown upwards on a smooth inclined plane with an initial speed of 10 m/s. The angle of inclination of the plane to the horizontal is 30o. If g = 10 m/s2, then if the mass of the object is 2 kg, the momentum of the object after 1 second is…

Known:

Initial velocity (vo) = 10 m/s

Angle = 30o

Acceleration due to gravity (g) = 10 m/s2

Mass (m) = 2 kg

Wanted: Momentum (p)

Solution:

Momentum Formula

P = m v = (2 kg)(10 m/s) = 20 kg m/s

Momentum is not depend on weight (w = mg).

3. A bullet is fired with a speed of 10 m/s. If the mass of the bullet is 20 grams, calculate the momentum of the bullet.

Known:

Bullet mass (m) = 20 grams = 20/1000 kg = 0.02 kg

Speed (v) = 10 m/s

Wanted: Momentum (p)

Solution:

Momentum formula

p = m v = (0,02 kg)(10 m/s) = 0,2 kg m/s

1. What is momentum? Momentum, usually denoted by ‘p’, is the product of an object’s mass (m) and its velocity (v). It is a vector quantity, with both magnitude and direction.
2. What is the unit of momentum in the SI system? The SI unit of momentum is kilogram meter per second (kg.m/s).
3. What is the importance of momentum in physics? Momentum is a fundamental concept in physics. It helps in understanding collisions and explosions (via the law of conservation of momentum), and forms the basis of Newton’s laws of motion.
4. How is the momentum of a system of particles calculated? The momentum of a system of particles is the vector sum of the momenta of each individual particle. If P is the total momentum, it is given by P = Σ pᵢ, where pᵢ is the momentum of the iᵗʰ particle.
5. What is the principle of conservation of momentum? The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.
6. Can an object have momentum if its speed is zero? No, an object with zero speed has zero momentum because momentum is the product of mass and velocity. If either mass or velocity is zero, the momentum is zero.
7. How does momentum relate to Newton’s second law? Newton’s second law can be expressed in terms of momentum: the net external force acting on an object is equal to the rate of change of its momentum. Mathematically, F = dp/dt.
8. What happens to the momentum of a system when two bodies collide? In a collision, the total momentum of the system (the sum of the momentum of each body) before the collision is equal to the total momentum after the collision, provided no external forces are acting. This is due to the conservation of momentum.
9. What is the difference between elastic and inelastic collisions regarding momentum? In both elastic and inelastic collisions, total momentum is conserved. However, in an elastic collision, kinetic energy is also conserved, while in an inelastic collision, kinetic energy is not conserved.
10. What is impulse and how is it related to momentum? Impulse, usually denoted by ‘J’, is the product of force (F) and the time duration (Δt) for which it is applied. It is equal to the change in momentum of the object. Mathematically, J = FΔt = Δp.
11. Why do we say momentum is a vector quantity? Momentum is a vector quantity because it has both magnitude and direction. The direction of the momentum vector is the same as the direction of the velocity vector.
12. How does an increase in velocity affect momentum? An increase in velocity will cause an increase in momentum, as momentum is directly proportional to velocity, given a constant mass.
13. What happens to the momentum of a rocket when it ejects fuel? As a rocket ejects fuel, the rocket’s velocity and thus momentum increase in the opposite direction. This is a consequence of the conservation of momentum.
14. What is angular momentum? Angular momentum is the rotational analog of linear momentum. For a single particle, it is the product of the particle’s momentum and the perpendicular distance from the rotation axis.
15. Is momentum always conserved in collisions? Yes, momentum is always conserved in collisions as long as no external forces are acting on the system.
16. What is the effect of mass on momentum? Momentum is directly proportional to mass, given a constant velocity. Hence, if the mass of an object increases, its momentum will also increase, provided its velocity remains constant.
17. Can momentum be negative? Yes, momentum can be negative. Momentum is a vector quantity, and the sign of the momentum depends on the direction of the velocity vector. A negative momentum simply means the object is moving in the opposite direction.
18. How is the momentum of a photon calculated? Even though a photon has zero rest mass, it has momentum due to its wave characteristics, given by p = h/λ, where h is Planck’s constant and λ is the wavelength of the photon.
19. How do airbags in cars use the principle of momentum? Airbags increase the time taken for the driver to come to rest during a collision, reducing the force experienced due to F = Δp/Δt. This decreases the likelihood of injury.
20. What is relativistic momentum? In Einstein’s theory of relativity, the momentum of an object moving with a high velocity (close to the speed of light) is given by p = γmv, where γ = 1/√(1 – v²/c²), v is the velocity of the object, c is the speed of light, and m is the object’s rest mass. This differs from classical momentum because γ increases without limit as v approaches c, so momentum increases significantly at high speeds.