Assume two identically sized and weighed markers are thrown to you at varying speeds. Which marker will cause you the most harm? Or will you be able to conveniently halt at whatever marker?
If you believe that both markers will harm you equally, you are mistaken. Because the marker travelling at a faster rate will inflict more damage on you than the marker moving at a slower rate.
The quantity of motion of objects of similar masses is determined by their velocities rather than their mass. In the absence of external forces, momentum is an unchanging quantity.
You must describe a parameter that changes if you would like to characterize change in a system. The agents of change are forces, and the attribute that is altered is momentum.
The majority of current physics may be deduced from these basic notions. As a result, the concept of momentum allows us to examine both linear and circular motion of objects in great detail. Without the concept of momentum, studying moving objects is impossible.
Momentum:
Definition
"Linear momentum, also known as translational momentum, is the product of a body's mass and velocity in classical mechanics."
It is a vector quantity and its direction is always towards the direction of velocity of body. It is also called the quantity of motion. Quantity of motion depends upon two things
- Mass of body (m)
- Velocity of body (v)
Formula
If a body having mass m is moving with velocity v then the quantity of motion or momentum of the body will be
P = mv
Where P is momentum of body and m is mass of body and v is velocity of body.
By reforming this formula the value of mass and velocity can also be determined if the other quantities are given.
For mass = m = P/v
For velocity = v = P/m
SI unit
The SI unit of quantity of motion is kg.m/s which is also equal to Ns.
Momentum in terms of Newton’s second law:
Consider that a force acts on a body having mass m. The force produces acceleration in body and it starts moving with initial velocity Vi. After some time t the body stops due to opposition in motion with final velocity Vf then according to Newton’s second law of motion
F = ma
As we know that time rate of change of velocity is acceleration hence
F = m (Vf - Vi/t)
F = mVf - mVi /t
As we know that P = mv so
F = ΔP/t
Or
F = ΔM/t
Where ΔM is change in momentum, t is time taken and F is applied force. Above equation shows that the applied force always changes or tends to change the momentum of a body.
Impulse
The change in momentum is also called impulse. It is also a vector quantity and its direction is also along the direction of velocity
How to calculate the problems of momentum?
Example 1: For change in momentum
Calculate the momentum shift of a 1200kg automobile that collides with a bus with a force of 110N in 12 seconds.
By using formula
Step 1: write given data values
Change in momentum = ΔP =?
Time = t = 12s
Force = F = 110N
Step 2: write the general formula
F = ΔM /t
Step 3: Rewrite the general formula for change in momentum
ΔP = ΔM = F × t
Step 4: Put the given data values in above formula
ΔP = ΔM = 110 × 12
ΔP = ΔM = 1320kg.m/s
Hence the change in momentum is 1320kg.m/s
By using online Momentum calculator
The solution to the above problem can also be find by using momentum calculator. Momentum calculator allows us to solve momentum related problems quickly and in an efficient manner.
It reduces the problem to simple steps and enables the students to devote more time in understanding the problem.
Example 2: For velocity
The parking brake on a 1200kg vehicle has failed, allowing the vehicle to accelerate at 7800kg.m/s. What is the vehicle's top speed?
Solution
Step 1: write given data values
Momentum = P = 7800kg.m/s
Velocity = v =?
Mass = m = 1200kg
Step 2: write the general formula
P = mv
Step 3: Rewrite the general formula for velocity
v = P/m
Step 4: Put the given data values in above formula
v = 7800/1200
v = 6.5m/s
Hence the velocity of vehicle is 6.5m/s.
Example 3: For mass
A toy projectile gun fires a dart with a momentum of 0.140kg.m/s and a velocity of 4m/s. What is the dart's mass in grams?
Solution
Step 1: write given data values
Momentum = P = 140kg.m/s
Velocity = v =4m/s
Mass = m =?
Step 2: write the general formula
P = mv
Step 3: Rewrite the general formula for mass
m = P/v
Step 4: Put the given data values in above formula
m = 0.140/4
m = 0.035kg
Conversion
m = 0.035 × 1000g
m = 35g
Hence the mass of dart is 35kg.
Example 4: For momentum
An automobile with a mass of 200 kg collides with a bus and comes to a halt. Find the momentum with which the car collides with the bus if the car's velocity is 100 m/s.
Solution
Step 1: write given data values
Mass = m = 200kg
Velocity = v = 100m/s
Step 2: write the general formula
P = mv
Step 3: Put the given data values in general formula
P = 200kg × 100m/s
P = 20000kg.m/s
Hence the momentum of the car at the time it strikes with the bus is 20000kg.m/s.
Summary:
Momentum is a preserved quantity that can deal with systems even when the precise mechanical energy is unknown. Momentum is a useful instrument for forecasting the behaviour of physical systems.
It is a member of the same family as kinematics, forces, and energy. When compared to energy, which is a conserved scalar, and forces, which are only conserved locally, there is a significant difference.
Overall, the concept of momentum as a characteristic that remains constant in the absence of external forces is useful because it defines the most significant and defining property of every system that must be examined in order to comprehend changes in the system.
As mentioned above the problems related to momentum can be solved by momentum calculator. By just providing the required information you can calculate all momentum related problems easily.
By Mia Emma
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