Question

21. The work done by a force acting obliquely is given by the formula: W = F cos tetha x S. What will
happen to the work done if angle between the direction of force and motion of the body is
increased gradually? Will it increase, decrease or remain constant?​

Answer 1

Solution -

We know that the work done by a force acting obliquely is given by the formula:

To Find -

What will happen to the work done if angle between the direction of force and motion of the body is increased gradually?

Will it increase, decrease or remain constant?

Concept Used -

Trigonometry

Here, in the formula , , Force and Displacement are constant quantities .

The value of Varies.

Now,

We have the following condition -

The angle between the direction of force and motion of the body is increased gradually.

Cos is an increasing function .

Domain € [ -1 , 1 ]

Here, the given angle can't be negative .

The minimum value of Cos is 1

It then decreases till the interval 2π

So,

The work done will decrease .

Answer -

The work done will decrease if angle between the direction of force and motion of the body is increased gradually.

_________________________

Answer 2

Answer:

Work Done

Work done on an object is defined as the product of the magnitude of the force acting on the body and the displacement in the direction of the force. W = F.s

If a force acting on a body causes no displacement, the work done is 0. For example, pushing a wall.

Work Done

To know more about Work, visit here.

Energy

Energy is defined as the ability to do work. Its unit is the same as that of work.

SI unit of energy or work = Joule (Nm) or Kgm2s−2.

Energy has different forms: Light, heat, chemical, electrical or mechanical.

Mechanical energy is the sum of:

(i) Kinetic energy (K.E)

(ii) Potential energy (P.E)

To know more about Energy and its type, visit here.

Kinetic Energy

Objects in motion possess energy and can do work. This energy is called Kinetic Energy.

F = ma.

Also W = F.s

⇒ From the 2nd equation of motion v2−u2=2as,

⇒ we get s = v2−u22a ⇒ Substituting equation for work done by a moving body,

⇒ we get W =m.a * v2−u22a

Or

⇒ Kinetic Energy = K.E= 12 mv2 (taking initial velocity u=0)

When two identical bodies are in motion, the body with a higher velocity has more K.E.

Kinetic Energy

To know more about Kinetic Energy, visit here.

Work-energy theorem

The work-energy theorem states that the net work done by a moving body can be calculated by finding the change in KE.

⇒ W net = KE final − KE initial

⇒ Wnet= 12 m[v2−u2]

To know more about Work-Energy Theorem, visit here.

Factors affecting kinetic energy

Mass

Velocity

Momentum.

Potential Energy

Energy can get stored in an object when work is done on it.

For example, stretching a rubber string. The energy that is possessed by a body by virtue of its configuration or change in position is known as Potential Energy.

Types of Potential Energy.

The potential energy of an object at a height.

When an object is raised to a certain height, work is done against gravity to change its position. This energy is stored as Potential Energy.

⇒W = F.s

⇒F = ma

In the case of increasing the height, F = mg

Therefore W (P.E) = mgh

⇒ ΔPE=mg(h final−h initial)

For More Information On Kinetic and Potential Energy, Watch The Below Video:

9,37,235

To know more about Potential Energy, visit here.

Law of Conservation of Energy

Law of conservation of energy states that energy can neither be created nor destroyed, but can be transferred from one form to another. The total energy before and after the transformation remains constant.

Total energy = KE + PE

For example: consider a ball falling freely from a height. At height h, it has only PE = mgh.

By the time it is about to hit the ground, it has a velocity and therefore has KE= 12 mv2. Therefore, energy gets transferred from PE to KE, while the total energy remains the same.

To know more about Law of Conservation of Energy, visit here.

Power

The rate of doing work or the rate of transfer of energy is called power. It is denoted by P

⇒ P = Wt

SI unit is Watt (Js−1).

Average power = Total energy consumed/Total time taken

The commercial unit of power is kWh i.e. energy used in 1 hour at 1000 Joules/second.

1kWh=3.6×106J