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Wonders of Physics

Tag Archives: Topic Energy Work Done Power


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Force required to pull the block up the inclined plane

There are 3 scenarios with slight variations.

Calculate the force F needed to pull the block up the inclined plane.

View the video below to understand how to solve these types of question.

You can also view the solutions below.

Click here to view another post related to this concept: work done to bring an object up


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N2007P1Q9 Pure Physics – Energy needed to pump water up a building

An apartment block receives water from a nearby reservoir. A pump is necessary to lift the water into a storage tank at the top of the building.

The gravitational field strength is 10 N / kg. How much energy does the pump supply to lift each kilogram of water into the tank?

GPE up 10 m

Solutions: 100J

Water will always find its own level. Hence with or without the pump, the water level in the pipe in the building will be of the same level as the reservoir. Hence, the pump is only needed to pump water up a height of 10m only (instead of the 50m).

Energy, E = mgh = 1 kg x 10 N/kg x 10m = 100 J


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Bullet embedded in wooden block

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At a training exercise, a policeman fires a pistol. A bullet of mass 10.0 g leaves the pistol horizontally at a speed of 500 ms-1. The bullet strikes and gets embedded in a stationary piece of wood of mass 1.0 kg which was suspended. Immediately after impact, the wood with the embedded bullet moves at a horizontal speed of 5.0 ms-1 and swings upwards to a vertical height of h from its initial position before stopping momentarily.

a) What is the initial kinetic energy of the bullet when it leaves the pistol?
b)What is the final kinetic energy of the wood and embedded bullet immediately after impact?
c) By comparing (a) and (b), what is the loss in kinetic energy? Account for this loss.
d) Calculate the vertical height, h, stating any assumption made. Assume the gravitational field strength is 10 N kg-1.

Solutions:

a) 1250 J

b) 12.6 J

c) 1240 J. The loss in kinetic energy is converted to heat and sound energy when the bullet strikes the wood and is embedded.

d) 1.25 m


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Energy calculation involving Work Done against friction

A box of mass 2 kg has an initial speed of 10 m/s at the foot of the ramp. Given that the friction along the ramp is 2 N, calculate the height h that it reaches when the speed of the box is 5 m/s. (g = 10 m/s2 )   work done inclined plane

Solutions:
For this question, the additional thing to note is the work done against friction. All the energy possesses by the box at bottom is KE. This KE will decrease and be converted to remaining KE at height h + gain in GPE + work done against friction.


To find the work done against friction, we need to find the distance moved by the box on the inclined ramp, d.

sin60 = h / d
d = h / sin60

Conservation of energy,
KE at bottom = KE at h + GPE at h + friction force
1/2mv2 = 1/2mv2 +   mgh  +   F x d
(1/2 x 2 x 102) = (1/2 x 2 x 52) + (2 x 10 x h) + (2 x h/sin60)
h     = 3.36 m


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Ratio of KE and GPE at various positions

A ball in thrown vertically up. D is the highest point the ball reached. Find the ratio of KE at B to the PE at C.   ratio of ke and gpe

Solutions: 1 : 1

To solve such question, you have to apply conservation of energy. In other words, total energy of ball at any positions (A, B, C and D) is the same (no air resistance etc). There is no way to find KE as no speed is given. So to find KE, you need to find it indirectly with the help of PE.

Understand the concept here as there can be many variations of question asked.


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Conservation of Energy – demo

This is a typical demo to illustrate conservation of energy. It will definitely be safe to remain stationary (if you release the ball from rest) as some of the energy of the ball will be converted to other forms like work done against air resistance. Hence, it will never reach the same height it is released, so will not never touch you.

Of course, if you give the ball a push, you are giving additional energy to the ball. That additional energy enable the ball to reach a greater height, hence most likely it will hit your face =)


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Work Done, Energy and Power are Scalar Quantities

Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.

Many have asked if Work Done is scalar or vector? Though from our textbook, Work Done = Force x distance in the direction of the force.

In other words, Work Done = Force x Displacement

We already know that Force is a vector. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the product (multiplication) of two vectors will result in a scalar or dot product.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore GPE  is a scalar.

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When considering KE, since KE = 1/2mv2 , similar to Method 1, v2 is actually velocity x velocity. Hence it product of 2 vectors, resulting in KE being a scalar.

Power = Energy Conversion/ time    or     Work Done / time,
since energy, work done and time are scalar, Power is a scalar quantity.

Other important note: Power = Rate of work done = Rate of energy conversion.


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Work Done, Energy and Power are Scalar Quantities

Work Done, Kinetic Energy (KE), Gravitational Potential Energy (GPE) and Power are all SCALAR quantities.

Many have asked if Work Done is scalar or vector? Though from our textbook, Work Done = Force x distance in the direction of the force.

In other words, Work Done = Force x Displacement

We already know that Force is a vector. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. In tertiary education, you will learn in details that the product (multiplication) of two vectors will result in a scalar or dot product.

Since it is out of syllabus, it will be good to use other ways to help you to understand and recall.

Method 1 Remember vector x vector will end up a scalar. Similar to (-)x(-) = (+) Method 2 Consider moving a box up to a certain height, work done or gain in GPE is constant regardless of the path it takes (diagonal or vertical). Hence direction is not important, therefore GPE  is a scalar.

Media_httpevantohfile_auomx

When considering KE, since KE = 1/2mv2 , similar to Method 1, v2 is actually velocity x velocity. Hence it product of 2 vectors, resulting in KE being a scalar.

Power = Energy Conversion/ time    or     Work Done / time,
since energy, work done and time are scalar, Power is a scalar quantity.

Other important note: Power = Rate of work done = Rate of energy conversion.


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Work done – Man jumps from height 3 m, what is the force exerted by his legs?

A boy of mass 40 kg jumps from rest from a platform of height 3 m. He lands by bending his knees and stops his body in 0.5 s after landing. What is the force exerted by his legs? man jump

Solutions: 620 N

To solve this question, you need to apply conservation of energy (COE) to find the kinetic energy (KE) that the boy possesses just before he reaches the ground.
After which, you can solve the question using (1) Conservation of energy or (2) Kinematics to solve.

Using COE to find the KE just before he reaches the ground.

Method 1: Using Conservation of Energy (COE)

Method 2: Using Kinematics


You must know these 2 methods and always think along this 2 directions when dealing with such questions.