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Work and Work Done by a Constant Force

Q: Convert \$1\$ joule to ergs.

Joule : SI system, erg:CGS systemWork = Force x Distance = Mass x Acceleration x Length = Mass x \$\dfrac{Length}{(Time)^2} \times Length\$Dimensions of work = \$[W] = [M^1L^2T^{-2}]\$\$\therefore a = 1, b = 2, c = -2.\$NowSI system CGS system\$M_1 = 1 kg\$ \$M_2 = 1 kg\$\$L_1 = 1 m\$ \$L_2 = 1 cm\$\$T_1 = 1s\$ \$T_2 = 1 s\$Here \$N_1 = 1, N_2 = ?\$\$\therefore Using\,\, N_2 = N_1\left [\dfrac{M_1}{M_2}\right]^a \left[\dfrac{L_1}{L_2}\right]^b \left[\dfrac{T_1}{T_2}\right]^c\$\$= 1\left[\dfrac{1kg}{1g}\right]^1 \left [\dfrac{1m}{1 cm}\right]^2 \left[\dfrac{1 s}{1 s}\right]^{-2}\$\$= 1\left[\dfrac{1000 g}{1 g}\right]^1 \left[\dfrac{100 cm}{1 cm}\right]^2\$\$= 10^7\$\$\therefore N_2 = 10^7\$So \$1 J = 10^7\$ erg

Q: A force of 7 N acts on an object. The displacement is 8 m, in the direction of the force. Consider force acting on the object through the displacement. What is the work done in this case ?

\$Given, \: force =7 \: N \;; \: displacement = 8 \: m \$\$Work \: done = Force \times Displacement\$ \$= 7 \times 8 = 56 \: J\$

Q: Explain Positive, Negative and Zero Work. Give one example of each.

POSITIVE WORK: The work done on an object is said to be positive work when force and displacement are in same direction.Example: When an object moves on horizontal surface, force and displacement acts in same direction. So, work done is positive.NEGATIVE WORK: The work done is said to be negative work when force and displacement are in opposite direction.Example: When an object is thrown upwards,the force of gravity is in downward direction whereas displacement acts in upward direction. ZERO WORK: The work done is said to be zero when force and displacement are perpendicular to each other or when either force or displacement is zero.Example: When we hold an object and walk, the force acts in downward direction whereas displacement acts in forward direction.

Q: Give two examples of (i) positive work (ii) negative work (iii) zero work

Positive work -1. Pushing a box through a distance.2. Lift a book through a height.Negative work -1. Work done by force of gravity on an object when lifted.2. Work done by friction when we walk.Zero work -1. Pushing a wall.2. Walking while holding an object.

Q: A cyclist comes to a skidding stop in \$10\ m\$. During this process, the force on the cycle due to the road is \$200\ N\$ and is directly oppose to the motion. (a) How much work does the road do on the cycle? (b) How much work does the cycle do on the road?

(a) Given Force on the cycle due to the road= 200 N and distance traveled during skidding before stopping =10 mWork done = force\$\times\$displacement=200\$\times\$10=\$-2000 J\$ (negative sign used as applied in the direction opposite to that of motion (b) zero

Q: A man pushes a wall and fails to displace it. He does :

\$\textbf{Hint}\$: We know work done in displacing the object is equal to the product of the force applied on the object and the distance traveled by it in the direction of force applied. Let us apply this concept to solve the problem. \$\textbf{Step 1}\$: We know \$Work \quad done(W)=F.S\$This is the work done by the man when he pushes the wall. Given that man pushes a wall and fails to displace it so displacement is zero i.e.., \$S=0\$\$\textbf{Step 2}\$: \$Work \quad done(W)=F.0=0\$So work done is zero. Thus option (D) is correct.

Q: A mass of \$10\ kg\$ is at a point \$A\$ on a table. It is moved to a point \$B\$. If the line joining \$A\$ and \$B\$ is horizontal what is the work done on the object by the gravitational force? Explain your answer.

Hint: Observe the angle between force of gravity and displacement.Explanation:Step 1: Concept used:Work done is given by:\$W= \overrightarrow {F}. \overrightarrow {S}\$\$W=F\ S\cos\theta\$where, \$F = \$ force applied\$S = \$ displacement\$\theta = \$ angle between the force applied and displacement.Step 2: Finding the work done:In the given problem, the force of gravity and displacement are perpendicular to each other. \$\theta =\$ \$90\$\$ \therefore W=0\$ Hence, the work done is zero.

Q: When a body moves with a constant speed along a circle, then which of the following is correct :

If the speed is constant then no force is acting in tangential direction. Only force acting is perpendicular to direction of velocity. Hence, work done will be zero.

Q: A body of mass \$m\$ kg is lifted by a man to a height of one meter in \$30\$ sec. Another man lifts the same mass to the same height in \$60\$ sec, calculate the ratio of the work done by the two men.

Both work the same amount of work because they lift the same mass to the same height.This ratio will be 1:1.Also, work does not depend on time.

Q: Convert 1 kWh into joules.

\$1 kWh = 1 kW \times 1 h\$ \$=1000 W \times 3600 s\$ \$= 3600000 J \$\$= 3.6 \times 10^6 J\$

Physics

definition

Work done by a constant force

When the force is constant, the work done is defined as the product of the force and distance moved in the direction of force.
Example: Suppose a body is kept on the frictionless surface and a force of constant magnitude of

10 N

is acting on it, due to the action of forces the body will completed a distance of

5

meter, then the work done will be given as

W = F s = 10 \times 5 = 50 J o u l e

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Convert 1 kWh into joules.

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definition

Work done by a constant force

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Examples of Work Done by a Constant Force

Convert 1 joule to ergs.

A force of 7 N acts on an object. The displacement is 8 m, in the direction of the force. Consider force acting on the object through the displacement. What is the work done in this case ?

Explain Positive, Negative and Zero Work. Give one example of each.

Give two examples of (i) positive work (ii) negative work (iii) zero work

A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 200 N and is directly oppose to the motion. (a) How much work does the road do on the cycle? (b) How much work does the cycle do on the road?

A man pushes a wall and fails to displace it. He does :

A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal what is the work done on the object by the gravitational force? Explain your answer.

When a body moves with a constant speed along a circle, then which of the following is correct :

A body of mass m kg is lifted by a man to a height of one meter in 30 sec. Another man lifts the same mass to the same height in 60 sec, calculate the ratio of the work done by the two men.

Convert 1 kWh into joules.

Convert $1$ joule to ergs.

A cyclist comes to a skidding stop in $10 m$ . During this process, the force on the cycle due to the road is $200 N$ and is directly oppose to the motion.
(a) How much work does the road do on the cycle?
(b) How much work does the cycle do on the road?

A mass of $10 k g$ is at a point $A$ on a table. It is moved to a point $B$ . If the line joining $A$ and $B$ is horizontal what is the work done on the object by the gravitational force? Explain your answer.

A body of mass $m$ kg is lifted by a man to a height of one meter in $30$ sec. Another man lifts the same mass to the same height in $60$ sec, calculate the ratio of the work done by the two men.