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Force Energy

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Force Energy

In simple terms, a force is nothing but a push or a pull. In scientific terms, a force is a movement produced by an object resulting from its interaction with another object or a field, such as an electric or gravitational field.

Force Energy and Moments A man pushing and pulling a chair StudySmarterFigure 1. A force can be a push or a pull on an object. Source: BruceBlaus, Wikimedia Commons (CC BY-SA 4.0).

Of course, a force is not just used to push or pull objects. We can, in fact, perform three types of functions with a force.

  • Changing the shape of an object: if, for instance, you bend, stretch, or compress an object, you change its shape.
  • Changing the speed of an object: if, while riding a bicycle, you increase the peddling or someone pushes you from behind, the speed of the bicycle increases. Exerting a stronger force thus causes the bicycle to accelerate.
  • Changing the direction in which an object is moving: in a cricket match, when a batsman hits the ball, the force exerted by the bat causes the direction of the ball to change. Here, a force is used to change the direction of an already moving object.

What is energy?

Energy is the ability to do work, while work is equal to the force being applied to move an object a certain distance in the direction determined by that force. So, energy is how much of the work is applied to the object by that force. The unique thing about energy is that it can be transformed.

Conservation of energy

The conservation of energy states that energy is only transferred from one state to another so that the total energy of a closed system is conserved.

For example, when an object falls, its potential energy is converted to kinetic energy, but the total sum of both energies (the mechanical energy of the system) is the same at every instant during the fall.

Force, Energy and Moments Diagram of a rollercoaster going up a hill and its velocity StudySmarter. Figure 2. Conversion from kinetic energy to potential energy in the case of a rollercoaster. Source: Guy vandegrift, Wikimedia Commons (CC BY-SA 3.0).

What is a moment?

The turning effect or a force produced around a pivot is called the moment of a force or torque. Examples of pivots are the hinges of an opening door or a nut turned by a spanner. Loosening a tight nut and a door opening around a fixed hinge both involve a moment.

Force Energy and Moments Diagram showing the Moment of a force StudySmarterFigure 3. Force at a distance from a fixed pivot produces a moment. Source: Usama Adeel, StudySmarter.

While this is a rotatory motion around a fixed pivot, there are also other types of turning effects.

What are the types of moments of a force?

Apart from the rotatory aspect, we also need to note the direction in which the object moves. For instance, in the case of an analogue clock, all its hands rotate in the same direction around a fixed pivot located in its centre. The direction, in this case, is a clockwise one.

Clockwise moment

When a moment or a turning effect of a force about a point produces a clockwise movement, that moment is clockwise. In calculations, we take a clockwise moment as negative.

Anticlockwise moment

Similarly, when a moment or a turning effect of a force about a point produces an anticlockwise movement, that moment is anticlockwise. In calculations, we take an anticlockwise moment as positive.

Force Energy and Moments A diagram showing clockwise and counter clockwise directions StudySmarterFigure 4. Clockwise and anticlockwise movements. Source: Wikimedia Commons (Public Domain).

How do we calculate a moment of a force?

The turning effect of a force, also known as torque, can be calculated by the formula:

  1. T = torque.
  2. r = distance from the applied force.
  3. F = applied force.
  4. 𝜭 = Angle between F and the lever arm.

Force Energy and Moments Diagram showing a force applied on a lever at an angle StudySmarterFigure 5. Moments applied to a perpendicular lever (F1) and one that operates at an angle (F2). Source: Usama Adeel, StudySmarter.

In this diagram, two forces are acting: F1 and F2. If we want to find the moment of force F1 around pivot point 2 (where force F2 acts), this can be calculated by multiplying F1 by the distance from point 1 to point 2:

However, to calculate the moment of force F2 around pivot point 1 (where force F1 acts), we have to improvise a little. Have a look at Figure 6 below.

Force Energy and Moments Diagram of a resolution of a vector StudySmarterFigure 6. Resolution of the F2 vector to calculate the moment of force F2. Source: Usama Adeel, StudySmarter.

F2 is not perpendicular to the rod. We, therefore, need to find the component of the force F2 that is perpendicular to the line of action of this force.

In this case, the formula becomes F2sin𝜭 (where 𝜭 is the angle between F2 and the horizontal). So, the formula to calculate the torque around the force F2 is:

The principle of moment

The principle of moment states that when a body is balanced around a pivotal point, the sum of the clockwise moment equals the sum of the anticlockwise moment. We say that the object is in equilibrium and will not move unless either one of the forces changes or the distance from the pivot of either of the forces changes. See the illustration below:

Force Energy and Moments Diagram showing an equilibrium of moments StudySmarterFigure 7. Examples of equilibrium. Source: Oğulcan Tezcan, StudySmarter.

Calculate the distance from the pivot of the force 250N that must be applied for the seesaw to be balanced if the force on the other end of the seesaw is 750N with a distance of 2.4m from the pivot.

The sum of clockwise moment = the sum of anticlockwise moment.

Hence, the distance of the force 250N has to be 7.2m from the pivot for the seesaw to be balanced.

What is a couple?

In physics, a moment of a couple is two equal parallel forces, which are in opposite directions from each other and at the same distance from the pivot point, acting on an object and producing a turning effect. An example would be a driver turning the steering wheel of their car with both hands.

The defining feature of a couple is that, although there is a turning effect, the resultant force adds up to zero. Hence, there is no translational but only rotational movement.

Force Energy and Moments Diagram of a moment Couple StudySmarterFigure 8. A couple is produced if two equal forces are acting in opposite directions at the same distance from the pivot point. Source: Usama Adeel, StudySmarter.

To calculate the moment of a couple, we need to multiply either one of the forces by the distance between them. In the case of our example above, the calculation is:

What is the unit of moment of a force?

As the unit of a force is Newton and the unit of the distance metres, the unit of moment becomes Newton per metre (Nm). A torque, therefore, is a vector quantity as it has a magnitude and a direction.

The moment of a force of 10N about a point is 3 Nm. Calculate the pivot distance from the line of action of the force.

Force Energy - Key takeaways

  • A force is a push or a pull on an object.
  • A force can change the shape of an object along with its speed and the direction in which it is moving.
  • Conservation of energy means that energy is only transferred from one state to another so that the total energy of a closed system is conserved.
  • The turning effect or a force produced around a pivot is the moment of a force or torque.
  • A moment can be in a clockwise or anticlockwise direction.
  • The principle of moment states that when a body is balanced around a pivotal point, the sum of clockwise moment equals the sum of anticlockwise moment.
  • A moment of a couple is two equal parallel forces, which are in opposite directions from each other and at the same distance from the pivot point, acting on an object and producing a turning effect.

Frequently Asked Questions about Force Energy

The moment of a force can be calculated by the formula:  


T = rfsin(𝜭)

Although moment and moment of a force have the same units, mechanically, they are not the same. A moment is a static force, which causes a non-rotational, bending movement under an applied force. A moment of a force, also called torque, is considered to rotate a body around a fixed pivot.

A moment of a force is also called a torque.

The law of moment states that, if a body is in equilibrium, meaning that it is at rest and non-rotational, the sum of clockwise moments equals the sum of anticlockwise moments.

Yes. Energy has a unit of Joule, which is equal to the force of 1 Newton acting on a body through a distance of 1 metre (Nm). This unit is the same as the moment.

Final Force Energy Quiz

Question

What is a vector?

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Answer

A quantity that has magnitude and direction.

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Question

A vector v is given. The horizontal component of v is vx, while the vertical component of v is vy. The vector v has an inclination angle of a. Which equation helps us determine vx?

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Answer

vx = v * cos (a).

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Question

A vector v is given. The horizontal component of v is vx, while the vertical component of v is vy. The vector v has an inclination angle of a. Which equation helps us find vy?

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Answer

vy = v * sin (a).

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Question

When determining the resultant vectors by using scale diagrams, how should we connect the vectors?

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Answer

Tip-to-tail.

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What is adding two vectors together called?

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Answer

Finding their resultant.

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What are the two ways we can add two vectors together?

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Using scale diagrams or trigonometry.

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Which of the following quantities is not a vector?

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Energy.

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When do we need to resolve vectors into components?

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In complex vector problems.

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Into which two components can we resolve a vector?

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Into a vertical and a horizontal component.

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Speed is a vector quantity. True or false?

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False.

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In which conditions can we use the Pythagorean Theorem to find the resultant of two vectors?

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When they are perpendicular to each other.

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Velocity is a vector quantity. True or false?

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True.

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Is force regarded as a vector quantity?

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Yes, it is.

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Under what condition is energy conserved?

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Energy is conserved in a given condition that the system is closed.

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Question

What is Kinetic Energy?

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Answer

Kinetic Energy is defined as the Energy possessed by a body by virtue of its state of motion.

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What is Potential Energy?


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Potential Energy is defined as Energy possessed by a body of a definite mass by virtue of its position in the presence of a gravitational field.

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What is Energy Dissipation?


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Answer

The loss of energy while energy transfers is known as Energy Dissipation.

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What is Elastic Energy?


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The Energy possessed by a body to retain its original configuration.

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What is Chemical Energy?


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The Energy possessed by a chemical substance.

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What is nuclear energy?


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Answer

Energy possessed by the nucleus of an atom.

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What is Tidal Energy?


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Answer

Energy possessed by the flowing water.

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Question

Give an example of mechanical energy converted to electrical energy.


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Answer

Power generator.

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Give an example of electrical energy converted to mechanical energy.


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Answer

Electrical mixer.

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Give an example of chemical energy converted to mechanical energy.


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Answer

Fuel engine.  

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Give an example of electrical energy converted to heat energy.


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Answer

Electric heater.        

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Give an example of electrical energy converted to light energy.      


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Answer

Light bulb.

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Question

Which angle will produce the maximum range in a projectile motion?

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Answer

θ = 45°

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Which of the following launch angles would produce the greatest height covered by an object?

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θ = 60°

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To get the minimum range, at which angle should an object be launched?


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θ = 0°

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Question

Suppose an object is released at an angle and hits the ground at the same level. What is the relation between the initial velocity and the final velocity of the object?


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Both velocities will be equal.

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The path taken by a projectile motion is referred to as:


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Parabolic.

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From the following options, choose the one which is not an example of a projectile motion.


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A car moving on a straight road.

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An object is thrown vertically from the edge of a cliff at a height of 60m with a velocity of 5m/s. Calculate the total time taken for the object to reach the bottom. Assume g = 10m/s2.

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3 seconds.

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What are the two forces that can influence projectile motion? 

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Air resistance and gravity.

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The x and y components in a projectile motion are independent of one another. True or false?

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True.

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Question

An object is thrown at an angle of 30° with a velocity of 20m/s. What is the vertical component of this projectile?

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Answer

20sin30 = 10m/s

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Question

You have two similar objects. One of them is released while the other is thrown horizontally at the same time from the same height. By not taking air resistance into consideration, will both objects reach the ground at the same time?


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Yes.

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An object is launched from the ground at an angle of 45° with a speed of 10m/s. What is the total time taken for the ball to hit the ground?


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Answer

1.414s

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A 50kg body is projected with a velocity of 25m/s at 60°. What is the range?


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50m

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When the air resistance is disregarded, the acceleration in the vertical direction of a projectile motion:


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Answer

Remains constant.

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Question

Which of the following has a magnitude but no direction?

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Scalar.

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How do you calculate the resultant vector if the vectors are in the same direction?

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Vectors in the same direction are added.

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What rule can you follow if two vectors are in a perpendicular direction and you have to calculate the resultant force?


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Answer

If two vectors are in a perpendicular direction and you have to calculate the resultant force, you can use the head-to-tail rule. 

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When do we need to resolve a vector into its components?


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We resolve a vector into its components if a vector at an angle to the horizontal (or the vertical) can be resolved into its components.

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Does the resolution of vectors happen only in two dimensions (x and y)?


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Answer

No, because a vector may have three components as well (x, y, z).

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Define a normal force.


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Answer

A normal force is the contact force that two objects experience when they come in contact with one another.

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Is a normal force equal and opposite in direction?


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Yes

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Question

What happens to the lines of forces if an object is in equilibrium? Choose the correct answer.

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All the lines of forces when extended intersect at one common point.

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Does the sum of all forces acting on a body in an equilibrium add up to zero?


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Answer

Yes.

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Question

Are mass and weight the same?


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Answer

No. Mass and weight are not the same. Mass is a scalar quantity, whereas weight is a vector quantity. 

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