Measuring Mass With A Balance
Difference Between Mass And Weight
People often get confused between mass and weight and they end up using these two terms interchangeably. However, mass and weight are two different terms and it is important to understand the difference between them. The difference between mass and weight is shown in the table given below.
| Mass can be easily measured using any ordinary balance.For example, beam balance, lever balance, pan balance, etc. | Weight can be measured by a spring balance or by using its formula given above. |
Did you know that we have different weights on the earth, the moon, and in space? However, our mass is the same everywhere.
Now, let us look at some important facts related to mass:
- Mass only has magnitude, hence, it is a scalar quantity.
- Weight has both magnitude and direction it is a vector quantity.
- Mass can also be defined as “stored energy in particles.”
- Mass represents the total atoms or particles that it contains.
From Force And Acceleration
The property of mass is also understood as the measure of a physical objects resistance to being accelerated by the application of an external force. This concept of mass is sometimes referred to as inertial mass. Inertia is the tendency for a moving body to continue in a constant state of motion, so inertial mass is a measure of how much inertia a body has and how difficult it is to change its state of motion. The relationship between mass, force, and acceleration is expressed by Newtons second law of motion F=ma. This mathematical relationship tells us that, in the face of a constant force, a more massive body will accelerate more slowly. By measuring the force applied to a body and measuring the observed acceleration, we can calculate the mass of the body.
For example, say that we apply a 748 N force to a metal cube, and we measure its acceleration as 21m/s2. What is the mass of the metal cube? We can figure calculate the mass by dividing the magnitude of the force by the magnitude of acceleration so:
m=F/a
So we know that the metal cube must have a mass of 35.62 kg.
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What Is The Mass Of An Object
The mass of an object or body is the physical measure of the total amount of matter present in it.
The mass is a constant quantity which means that no matter where you go on Earth, it remains the same. It is the quantity of matter of any given body. The general unit of mass is in grams or kilograms.
What Is The Unit Of Mass
There are various units for calculating mass, like, kilograms, grams, lbs, pounds, etc., but the SI unit of mass is “kilograms” or kg. Every unit of mass can be converted to other units by using a proper conversion formula without affecting the meaning and essence of the quantity to be measured.
Note: 1kg is equal to 2.20462 pounds.
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Newtons Laws Of Motion
- Explain the difference between mass and weight
- Explain why falling objects on Earth are never truly in free fall
- Describe the concept of weightlessness
Mass and weight are often used interchangeably in everyday conversation. For example, our medical records often show our weight in kilograms but never in the correct units of newtons. In physics, however, there is an important distinction. Weight is the pull of Earth on an object. It depends on the distance from the center of Earth. Unlike weight, mass does not vary with location. The mass of an object is the same on Earth, in orbit, or on the surface of the Moon.
How To Calculate Mass From Force And Velocity Using Third Kinematic Equation Of Motion:
The following is the third kinematic equation of motion:
v2 = u2 + 2ad.
It shows the relationship between the initial and final velocity. We may now apply Newtons Second Law ) to this equation and obtain:
v2 = u2 + 2d
v2 u2 = 2d .
Thus, using the third kinematic equation, the mass of an object can be calculated as follows:
.
If you know the distance travelled by an object when its velocity v varies from its initial velocity u as a result of force F. In that instance, we can use the third kinematics equation of motion to calculate its mass.
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Can Net Force Be Negative
Net force can be both positive and negative. Net force is the sum of the vectors of all the individual forces that act on an object. Forces are always positive in magnitude, but, to make net force easier to calculate, we assume that forces aiming at opposite directions have different signs. Usually, we say that forces aiming to the right are positive, and to the left – negative. So, if you have two forces opposite in direction acting on an object and the net force aims to the left, you could say that the net force is negative.
What Is The Difference Between Balanced And Unbalanced Forces
Balanced forces have the same magnitude but opposite direction. They balance each other, and so cancel each other out. A classic example of balanced forces would be the gravitational force and the normal force acting on an object placed on a horizontal surface. Balanced forces cause no change in the direction or speed of an object.
Unbalanced forces don’t have the same magnitude. If an unbalanced force acts on an object, it impacts the object’s motion. For example, if something falls, it’s because of gravitational force. Air resistance force counteracts gravity, but it doesn’t balance it out if the object is too heavy.
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How To Find Force
Let’s look at a few exercises so that nothing can surprise you in your physics class.
1. Find the accelerating and retarding force:
A cheetah has a mass of 50 kg. It accelerates from rest to 50 km/h in 3 seconds. Then it starts steadily slowing down and stops after 8 seconds.
-
Accelerating force:
50 km/h is equal to 13.89 m/s .
Acceleration is equal to difference in velocity over time:
a = / 3 s = 4.63 m/s2
Calculate accelerating force:
Fa = m * a = 50 kg * 4.63 m/s2 = 231.5 N
-
Retarding force:
a = / 8 s = -1.74 m/s2
Fr = 50 kg * -1.74 m/s2 = -87 N
Retarding force is negative, because it has an opposite direction to the accelerating force.
2. How much force do you need to accelerate an object by 8 m/s2? What about when the object is three times heavier? How does it affect the force?
-
F1 = 2 kg * 8 m/s2 = 16 N
-
F2 = 3 * 2 kg * 8 m/s2 = 48 N
If the mass is three times heavier, the force needs to be three times bigger.
Relation Between Weight And Mass
Consider a body having large mass and large weight. Example of this situation is a large object which is hard to throw because the weight of this object is large.
Therefore, the relation between weight and mass can be derived with the help of Newtons second law which explains that the free falling object has an acceleration g as the magnitude.
If an object with a mass of 1kg falls with an acceleration of 9.8 ms-2, then the magnitude of the force is given as :F = ma
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Is Acceleration A Force
Acceleration is not a force. Acceleration is the change of velocity over time. Same as force, acceleration is a vector, so it has both magnitude and direction. According to Newton’s second law of motion, acceleration is proportionate to force: F = m ⨠a. The direction of an object’s acceleration is determined by the net force’s direction acting on that object.
How To Calculate Mass From Force And Velocity Using Centripetal Force:
When a body moves in a curved route, centripetal force exerts on it, which has an inward direction, or we might say towards the center. The centripetal force which acts on a body moving along a circular path of radius R is given by:
.
Thus, the mass of an object moving on a circular path is given by:
.
Here, Fc is used for centripetal force.
This is how the mass of an object moving on a circular path can be calculated using centripetal force, velocity, and the radius of the path.
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Why Do Objects Tend To Rotate Around Their Center Of Mass
Lets go back to our flying rod example. If the rotation of a free body would not occur around its center of mass, then this point would not only translate but also rotate around the new rotation axis, as shown in the next image. Now, a rotation of any point implies it is constantly accelerating, since its velocity is always changing direction. Remember acceleration is the change in time of either the magnitude or the direction of a bodys velocity vector.
Now, for an acceleration to exist, there has to be a force causing it. This force would have to be constantly applied to the center of mass to change its direction of movement. Nevertheless, this is not possible in our flying rod example, since no forces other than gravity are acting on it once it leaves your hand. You might ask yourself, can gravity cause the change in direction of the center of mass? The answer is no, since it is a force with a constant direction: towards the center of The Earth.
In summary, the rotation of a free body around an axis different from its center of mass is simply not possible, because it would require the existence of an additional external force that causes an acceleration of the center of mass.
Force Definition And The Force Equation
What is force?
Force is any interaction that, if unopposed, can change the motion of an object.
If asked, “What is force?” a non-physicist would probably think about pushing and pulling. A physicist would think about the change in the velocity of an object. To understand why let’s look at the force equation:
- a is the acceleration of the object expressed in metre per second squared
- m is the mass of an object in kilograms and
- F is the force measured in Newtons .
Acceleration is the change of velocity over time. And, as you see from the force formula, the greater the force, the greater the acceleration. So, if something is speeding up, for example, a car, it can impart a significant force if it crashes on another car. This force is proportional to the car’s mass and its acceleration. Another example would be the human punch force, where the mass and acceleration of the body are directly proportional to the impact force.
To use the force calculator, input two of these variables: mass, acceleration, or force in any unit and get the missing number in a blink of an eye.
If you’re calculating force on your own, always use the SI system to avoid mistakes. What is the SI unit of force? It’s Newton – named after Isaac Newton – mathematician, physicist, and discoverer of gravity. In SI base units, one Newton is equal to:
To learn more about force units go to our force converter.
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How To Calculate The Position Of The Center Of Mass
The center of mass is defined as the point of space in which the weighted distances to all of the masses that form a body or a system of bodies adds to zero. This point of space, C, can be determined for any collection of masses by calculating its different components along the x-, y- and z-axes.
For a single body of homogeneous density, the center of mass lies on the same point as the centroid. This is the geometrical center of the body. For simple regular shapes, like spheres, squares, rings, cylinders, etc., the centroid is located where two or more axes or planes of symmetry cross each other. The following image shows some examples of the centroids of some regular shapes, with some of their symmetry axes shown as dotted lines:
Notice the centroid, and therefore the center of mass, of a ring would lie in its middle, where there is no material. This is because the center of mass is a concept and not necessarily a physical point inside a body. The effect of applying a force to the edge of the ring will be a rotational movement around its center of mass. If you want to displace the ring, you will have to exert a force that passes through the center of mass.
Lets consider our initial example: Pluto and Charon. The following image summarizes the situation. Pluto has an approximate mass of 131021kg, and Charon one of 1,591021kg. Both bodies are separated by a distance of 19570 km.
| Cx=m1x1+m2x2m1+m2=131021kg +1,591021kg 131021kg+1,591021=2132,7 km |
Center Of Mass Formula
Before to start, let us get some terms out of the way. Also, we need to know the center of mass for an object or a set of objects. It is the point about which the entire mass of the system is equally distributed. In this regard, the center of gravity is also important to know. It refers to the point about which the forces of gravity are balanced. In physics center of mass of an object is very important to find accurately. In this article, we will discuss the center of mass formula with examples. Let us begin learning!
Table of content
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How To Calculate Weight From Mass
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The weight of an object is the force of gravity exerted on that object. The mass of an object is the amount of matter it has, and it stays the same wherever you are, regardless of gravity.XResearch source That’s why an object that has 20 kilograms of mass on earth also has 20 kilograms of mass while on the moon, even though it would only weigh 1/6 as much. It weighs 1/6 as much on the moon because the force of gravity on the moon is 1/6 of what it is on Earth. Read on for information about and tips on calculating weight from mass.
Centre Of Mass Formula
We can extend the formula for the center of mass to a system of particles. We can apply the equation individually to each axis also.
Although the center of mass and the center of gravity often coincide, these are all different concepts. Meanwhile, the center of gravity and the center of mass are only equal when the entire system is subject to a uniform gravitational field.
We can use the above formula if we have pointed objects. On the other hand, we have to take a different approach if we have to find the center of mass of an extended object like a rod. Then we will consider a differential mass and its position and then integrate it over the entire length.
Where,
| Distance from the x-axis of ith object |
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Newton’s Laws Of Motion
Newton came up with three laws of motion that explain the movement of all physical objects. They are the basics of all classical mechanics, which is also known as Newtonian mechanics.
An object will remain at rest or continue to move in uniform motion unless acted upon by an external force.
Force exerted by an object equals mass times acceleration of that object: F = m * a.
When one body exerts a force on a second body, the second body exerts a force equal in magnitude and opposite in direction on the first body .