Saturday, March 2, 2024

# How To Calculate Force In Physics

## What Is The First Thing You Should Adjust If Needed When You Get Into A Car To Drive

Normal Force Physics Problems With Tension, Inclined Planes & Free Body Diagrams

What is the first thing you should adjust, if needed, when you get into a car to drive? When preparing to drive, you should first adjust your seat to ensure that you are in a comfortable position and can see the road clearly. Adjust your mirrors and steering wheel to be effective when your seat is fully adjusted.

## Example 2 What Is The Tension In A Tightrope

Calculate the tension in the wire supporting the 70.0-kg tightrope walker shown in Figure 6.

Figure 6. The weight of a tightrope walker causes a wire to sag by 5.0 degrees. The system of interest here is the point in the wire at which the tightrope walker is standing.

#### Strategy

As you can see in the figure, the wire is not perfectly horizontal , but is bent under the persons weight. Thus, the tension on either side of the person has an upward component that can support his weight. As usual, forces are vectors represented pictorially by arrows having the same directions as the forces and lengths proportional to their magnitudes. The system is the tightrope walker, and the only external forces acting on him are his weight w and the two tensions TL and TR , as illustrated. It is reasonable to neglect the weight of the wire itself. The net external force is zero since the system is stationary. A little trigonometry can now be used to find the tensions. One conclusion is possible at the outsetwe can see from part of the figure that the magnitudes of the tensions TL and TR must be equal. This is because there is no horizontal acceleration in the rope, and the only forces acting to the left and right are TL and TR. Thus, the magnitude of those forces must be equal so that they cancel each other out.

## 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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## The Meaning Of Centripetal Force

In the Physics tutorial “Kinematics of the Rotational Motion“, we discussed about centripetal acceleration that exists because of the change in direction of velocity vector during rotation. It was stressed that this kind of acceleration exists even when the object is rotating uniformly, i.e. at constant tangential speed. Furthermore, the vector of centripetal acceleration is always directed towards the centre of curvature as shown in the figure below.

The equation of centripetal acceleration is

v/t

where v is the change in velocity of the rotating object in two given instants and t is the time interval between these two instants.

The scalar form of the equation is

v2/r

where r is the radius of curvature. This is the reason why centripetal acceleration is often referred as “radial acceleration, ar”.

From Newton’s Second Law of Motion we known that where there is an acceleration, there is also a force causing it. Centripetal acceleration makes no exception to this rule as well. Therefore, it is obvious there must be a force causing the centripetal acceleration. This force is known as Centripetal Force, FC and it is the force responsible for keeping an object in rotation. It is in the same direction of centripetal acceleration, i.e. towards the centre of circle.

From Newton’s Second Law of Motion, we have:

where m is the object’s mass. In scalar form, the above equation is written as:

m × v2/rm × v2/r20 kg × 2/2 mm × v2/r

## How To Calculate Mass From Force And Velocity Using Third Kinematic Equation Of Motion:

The following is the third kinematic equation of motion:

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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## Determining Tension On A Single Strand

• 1Define the forces on either end of the strand. The tension in a given strand of string or rope is a result of the forces pulling on the rope from either end. As a reminder, force = mass × acceleration. Assuming the rope is stretched tightly, any change in acceleration or mass in objects the rope is supporting will cause a change in tension in the rope. Don’t forget the constant acceleration due to gravity – even if a system is at rest, its components are subject to this force. We can think of a tension in a given rope as T = + , where “g” is the acceleration due to gravity of any objects the rope is supporting and “a” is any other acceleration on any objects the rope is supporting.XResearch source
• For the purposes of most physics problems, we assume ideal strings – in other words, that our rope, cable, etc. is thin, massless, and can’t be stretched or broken.
• As an example, let’s consider a system where a weight hangs from a wooden beam via a single rope . Neither the weight nor the rope are moving – the entire system is at rest. Because of this, we know that, for the weight to be held in equilibrium, the tension force must equal the force of gravity on the weight. In other words, Tension = Force of gravity = m × g.
• Assuming a 10 kg weight, then, the tension force is 10 kg × 9.8 m/s2 = 98 Newtons.
• Ft = Fg + m × a
• Ft = 98 + 10 kg × 1 m/s2
• Ft = 108 Newtons.
• Fc = m × v2/r
• Fc =10 × 2.67 = 26.7 Newtons.
• So, our the total tension would be 98 + 26.7 = 124.7 Newtons.
• T = 980/15
• ## How To Calculate Speed From Force And Mass Using Newtons Second Law

Lets calculate speed from force and mass employing Newtons second law of motion.

Newtons second law connects the rate of velocity change or acceleration with applied force and mass. To calculate speed from Newtons second law, we first need to understand the difference between speed and velocity and then calculate the speed value from the rate of velocity change.

As per Newtons second law,

Whereas v0 is the initial velocity and v is the final velocity

Before calculating speed using Newtons law, lets comprehend the differences between speed and velocity.

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## Magnitude Of A Single Force Vector

To calculate the magnitude of force vectors, you use the components along with Pythagoras theorem. Think of the x coordinate of the force as the base of a triangle, the y component as the height of the triangle, and the hypotenuse as the resultant force from both components. Extending the link, the angle the hypotenuse makes with the base is the direction of the force.

If a force pushes 4 Newtons in the x-direction and 3 N in the y-direction, Pythagoras theorem and the triangle explanation show what you need to do when calculating magnitude. Using x for the x-coordinate, y for the y-coordinate and F for the magnitude of the force, this can be expressed as:

In words, the resultant force is the square root of x2 plus y2. Using the example above:

So, 5 N is the magnitude of force.

Note that for three-component forces, you add the z component to the same formula. So:

## How To Calculate Tension In Physics

Calculating Contact Forces Between Two Blocks Using Free Body Diagrams

In physics, tension is the force exerted by a rope, string, cable, or similar object on one or more objects. Anything pulled, hung, supported, or swung from a rope, string, cable, etc. is subject to the force of tension.XResearch source Like all forces, tension can accelerate objects or cause them to deform. Being able to calculate tension is an important skill not just for physics students but also for engineers and architects, who, to build safe buildings, must know whether the tension on a given rope or cable can withstand the strain caused by the weight of the object before yielding and breaking. See Step 1 to learn how to calculate tension in several physical systems.

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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.

## Friction Coefficient For Different Materials

The coefficient of friction is determined experimentally, but there are some values available in physics books. The table below contains the values for the coefficient of friction compiled from the references , and .

Coefficients of friction
0.03 0.60

For a better understanding on how to calculate the friction force, lets go through some practical examples.

## How To Calculate Mass From Force And Velocity Using Newtons Second Law:

The second law of Newton can be expressed in various ways. The statement says that when a force acts on an objector particle, the force is equal to the change in momentum over time. The following is an equation that can be used to express the statement:

Here, the letter p can be used to signify the momentum of an object or particle. However, we know that it is the product of the objects mass and velocity. As a result, its written mathematically as:

p = mv

We get the following when we substitute the above momentum equation in the force equation:

Now, mass increases only when an objects velocity reaches the speed of light. However, this is not the case here. Because the velocity of the particle or object is not very high, i.e. close to the velocity of light, the mass of the object remains constant. As a result, we assume that only velocity, not mass, changes with time. As a result, the equation above can be represented as:

.

F = ma.

Thus, in terms of force and velocity, the mass of an object can be calculated as follows:

.

Thus, from equation , if we know the force acting on the body and how velocity changes with time, it is easy to calculate mass using Newtons second law.

## Example: The Forces At The Top Of This Bridge Tower Are In Balance :

The cables pull downwards equally to the left and right, and that is balanced by the towers upwards push.

We can model the forces like this:

And when we put them head-to-tail we see they close back on themselves, meaning the net effect is zero:

The forces are in balance.

Forces in balance are said to be in equilibrium: there is also no change in motion.

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## How To Find Tension In Ropes While Pulling An Object

How to find the tension force on an object being pulled is just like when the object is hung. The only difference is that we first need to compute the acceleration of the entire system and sum all of the of forces along the horizontal. If the rope is at an angle from the level of the floor, we need to compute for the horizontal component of the pulling force too.

Let us take a look at the example below to better understand how to find the tension force in a rope pulling one or two objects. In this example, two objects are being pulled by a single applied pulling force. Another rope is pulling the second object, which is attached to the first object, as shown below:

This illustration shows that the masses of m and m are 3 kg and 2 kg, respectively. The sum of these two masses gives the total mass of the system, 5 kg. We also need to determine the horizontal component of the pulling force, T = 24 N, that is at an angle = 60°. If we use the trigonometric functions again, we can say that the horizontal component of the pulling force is equal to 24 N * cos, which is equal to 12 N. Now that we know the pulling force’s horizontal component and the total mass of the system, we can now calculate the acceleration, a, of the system as follows:

F = m * a a = F / ma = 12 N / 5 kg = 2.4 m/s²

## Limitations Of The Coulomb Model

The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area that this contact area is proportional to the normal force and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. It is a rule-of-thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility. Though the relationship between normal force and frictional force is not exactly linear , the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems.

When the surfaces are conjoined, Coulomb friction becomes a very poor approximation . In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications.

#### Negative coefficient of friction

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## Resolving Weight Into Components

Figure 3. An object rests on an incline that makes an angle with the horizontal.

When an object rests on an incline that makes an angle with the horizontal, the force of gravity acting on the object is divided into two components: a force acting perpendicular to the plane, w, and a force acting parallel to the plane,\textbf_. The perpendicular force of weight, w, is typically equal in magnitude and opposite in direction to the normal force, N. The force acting parallel to the plane, \textbf_, causes the object to accelerate down the incline. The force of friction, f, opposes the motion of the object, so it acts upward along the plane. It is important to be careful when resolving the weight of the object into components. If the angle of the incline is at an angle to the horizontal, then the magnitudes of the weight components are

w_=w \sin = mg \sin

w_=w \cos = mg \cos

Instead of memorizing these equations, it is helpful to be able to determine them from reason. To do this, draw the right triangle formed by the three weight vectors. Notice that the angle of the incline is the same as the angle formed between w and w. Knowing this property, you can use trigonometry to determine the magnitude of the weight components:

\cos=\frac_}

w_ = w \cos = mg \cos

\sin=\frac_}

w_ = w \sin = mg \sin

## How To Calculate Mass From Force And Velocity Using Work Energy Theorem:

How to Calculate Force | plus | How to Calculate Distance | Physics |

When the force is applied to an object, it moves a certain distance. As a result, according to the work energy theorem, the work done on the object to move this distance is equal to the kinetic energy gained by the object. In a nutshell, work is converted into energy. Putting it in mathematical terms:

W = K.E.

However, the work done on the object to move the distance d is as follows:

W = Fd.

And the kinetic energy of an object with velocity v is:

.

From, equations , and :

.

Thus, using the work energy theorem, the mass of an object is given by:

.

Thus, we can argue that finding mass from the work energy theorem is a special case of finding mass from the third kinematic equation where the objects initial velocity is zero, implying that it is initially thought to be at rest.

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## How To Calculate The Buoyant Force

Follow the simple process listed here to find out the buoyant force and they are as such

• Firstly, decide on the gravitational acceleration in which you want to find out the buoyancy.
• Later, choose the liquid you want to immerse the liquid in.
• Immerse the object in the liquid and find out the volume of displaced liquid
• Substitute all these values in the equation of Buoyancy Force i.e. B = * V * g
• Simplify the equation further and determine the buoyancy force easily.

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