Amount of movement: what is it, formula, exercises

The amountinmovement is greatness vector physics that is defined by the product of mass, in kilograms, and velocity, in meters per second. It is one of the most important magnitudes of Dynamics because it is related to other magnitudes, such as strength, impulse and kinetic energy. The amount of movement, which is also known as linear momentum, is dimensionally equal to the impulse quantity, whose unit of measure is kg.m/s or even N.s.

Such quantities are related to each other by the Newton's 2nd Law, which states that the net force on a body causes a variation in the amount of movement over a certain period of time. Also, according to the principle of conservation of momentum, we say that in systems that do not exhibit any dissipative forces, such as frictional force, the total momentum must be maintained.

Newton's pendulum is used to demonstrate momentum transfer.
Newton's pendulum is used to demonstrate momentum transfer.

Momentum Formulas

THE formula of the amount of movement defines that the pasta multiplied by the speed equals the timelinear of the body.

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Q – amount of movement or linear momentum (kg.m/s)

m – mass (kg)

v – speed (m/s)

Since the amount of movement is defined from the Newtonian laws of mechanics, the formula that relates net force to the change in momentum is as follows:

ΔQ – variation of the amount of movement

QF and Qi – initial and final movement quantities

Δt – time interval(s)

F – net force (N)

From the formula shown above, it can be seen that the vector of the variation in the amount of movement (ΔQ) has the same meaning as the resultant force vector (FR). Therefore, when a body is subject to a non-zero net force, its momentum will vary in the same direction and direction as the resulting force.

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Finally, the Kinetic energy can also be written in terms of momentum.. This representation of kinetic energy indicates that this energy can be written as the ratio between the square of the momentum and the mass of the body, multiplied by 2. Look:

ANDÇ – kinetic energy (J)

Lookalso:How to solve exercises on Newton's laws?

Conservation of momentum

THE conservation of momentum it is one of the most important principles of physics. According to this principle, in the absence of dissipative forces, the total amount of movement of a system must remain constant. This indicates that, in situations where they occur collisions, for example, the product of the mass and the velocity of the bodies must be equal before and after the contact between them - in these cases, we say that the collision was perfectly elastic.

In the figure, the momentum of bodies A and B is preserved after the collision.
In the figure, the momentum of bodies A and B is preserved after the collision.

In this case, the formula used to express the conservation of momentum is as follows:

mTHE inB masses of bodies A and B

vTHE and youB– speeds of bodies A and B before the collision

v'THE and seeB– speeds of bodies A and B after the collision

Lookalso: Impulse and amount of movement

Solved Exercises on Amount of Movement

Question 1) (Uerj) The graph below indicates the variation in the acceleration a of a body, initially at rest, and the force F acting on it.

When the speed of the body is 10 m/s, its amount of movement, in kg.m/s corresponds to:

a) 50

b) 30

c) 25

d) 15

Template: letter B.

Resolution:

First, you need to find out what the body's mass is from the graph and using the resultant force formula.

Finally, the exercise asks us to calculate the amount of movement when the body speed is 10 m/s. To do so, just do the following calculation:

Based on the result obtained, the correct alternative is the letter B.

Question 2) (Uece) Consider a wagon with a net cargo that is pulled by a locomotive on a straight horizontal track. Neglect friction and consider that the force applied by the locomotive to the car is constant. In case of leakage of this cargo, the linear moment of the assembly formed by the wagon and the load inside it:

a) it varies only by the application of force.

b) varies by the application of force and by the variation in mass.

c) it varies only by the loss of mass of the wagon.

d) does not vary even with change in mass.

Template: letter B,

Resolution:

As we have already seen, the net force applied to a body depends on the variation in the amount of motion, which in turn depends on both the mass and speed of the body. See the relationship between strength and amount of movement:

Question 3) (Fatec) In a class on the Airport Logistics course, the professor proposes to the students that they determine the amount of movement of the type 737–800 aircraft in a cruise flight, considering ideal conditions. For this it presents approximate values, provided by the aircraft manufacturer.

Information

Given away

Maximum takeoff mass

79,000 kg

Average cruise speed

720 km/h


Based on the data presented in the table, the approximate expected result is, in kg.m/s:

a) 1.6.107

b) 2.0.107

c) 2.6.107

d) 3.0.107

e) 3.6.107

Template: letter a.

Resolution:

The exercise resolution requires that the plane's speed be converted from kilometers per hour to meters per second. For that, the value of 720 km/h must be divided by factor 3.6. Then just multiply the mass and speed of the body.

By Rafael Hellerbrock
Physics teacher

Would you like to reference this text in a school or academic work? Look:

HELERBROCK, Rafael. "Amount of movement"; Brazil School. Available in: https://brasilescola.uol.com.br/fisica/quantidade-movimento-sua-definicao.htm. Accessed on June 27, 2021.

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