Question

1. Certain force acting on a 20 kg mass changes its velocity from
5 ms-1 to 2 ms-1. Calculate the work done by the force.
tohle Itis moved to​

Answer 1

Required Answer:

• Mass of the body = 20 kg
• Initial velocity, u = 5 m/s
• Final velocity, v = 2 m/s

According to work energy theoram,

• The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.

Kinetic energy is given by the expression,

$\cdot{ \underline{ \boxed{ \sf{E_k = \frac{1}{2} m {v}^{2} }}}}$

Now,

1) KE when velocity of object is 5 m/s:

= 1/2 (20)(5)² J

= 10 × 25 J

= 250 J

2) KE when velocity of object is 2 m/s

= 1/2 (20)(2)² J

= 10 × 4 J

= 40 J

According to theoram,

• Work done = Change in K.E.

Plugging the values of Initial and Final KE:

⇒ Work done = 40 J - 250 J

⇒ Work done = -210 J

*Here negative sign indicates that the force is acting opposite to the direction of motion of the object.

Answer 2

$\: \: \: \: \:{\Large{\bf{\underbrace{Required \; Solution}}}}$

${\large{\bold{\rm{\underline{Correct \: question}}}}}$

↪ Certain force acting on a 20 kg mass changes its velocity from 5 m/s to 2 m/s. Calculate the work done by the force.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

◕ Mass of body = 20 kg.

◕ Final velocity = 5 m/s

◕ Initial velocity = 2 m/s

${\large{\bold{\rm{\underline{To \; find}}}}}$

◕ Work done by the force

${\large{\bold{\rm{\underline{Solution}}}}}$

◕ Work done by the force = -210 J

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

◕ Formula to find Kinetic Energy

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

${\boxed{\boxed{\sf{Kinetic \: energy \: = \: \dfrac{1}{2} mv^{2}}}}}$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ Let's find the Kinetic energy

☀ Let us find Kinetic Energy when the velocity of the object is 2 m/s

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} mv^{2}}}$

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} (20)(2)^{2}}}$

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} (20)(4)}}$

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} (80)}}$

⇢ Kinetic energy = 40 Joules

${\pink{\frak{Henceforth, \: 40J \: is \: kinetic \: energy \: of \: object \: Velocity \: 2m/s}}}$

☀ Let us find Kinetic Energy when the velocity of the object is 5 m/s

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} mv^{2}}}$

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} (20)(5)^{2}}}$

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} (20)(25)}}$

⇢ ${\sf{Kinetic \: energy \: = \: \dfrac{1}{2} (500)}}$

⇢ Kinetic energy = 250 Joules

${\pink{\frak{Henceforth, \: 250J \: is \: kinetic \: energy \: of \: object \: Velocity \: 5m/s}}}$

~ Now as we know that,

⇢ Work done = Change in kinetic energy.

⇢ Work done = (45-250)J

⇢ Work done = -210 J

${\pink{\frak{Henceforth, \: -210J \: is \: work \: done}}}$

${\large{\bold{\rm{\underline{Additional \; information}}}}}$

★ Distance = It is the length of actual path covered by a moving object in a given time interval.

★ Displacement = Shortest distance covered by a body in a definite direction is called displacement.

→ Displacement may be positive, negative or zero whereas distance is always positive.

→ Distance is a scaler quantity whereas displacement is a vector quantity both having the same unit.

→ In general magnitude of displacement ≤ Distance.

★ Velocity = Velocity of moving object is defined as the displacement of the object in unit time interval i.e., velocity = Displacement/Time. It's vector quantity and it's SI unit is metre/second.

★ Acceleration = Acceleration of an object is defined as the rate of change of velocity of the object i.e., Acceleration = Change in velocity/Time. It's vector quantity and SI unit is m/s²

★ If Velocity decreases with time then acceleration is negative and known to be retardation.

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$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: magnetic \: flux \: is \: Weber}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: surface \: tension \: is \: \dfrac{N}{m}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: mechanical \: power \: is \: Watt}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto 1 \: horsepower \: = \: approx \: 746 \: watts}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Momentum \: is \: measured \: as \: the \: product \: of \: Mass \: and \: velocity}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto \pi 'pi' \: is \: calculated \: by \: Aryabhatta}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto One \: J \: = \: 0.24 \: cal}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Number \: of \: SI \: units \: are \: 7}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Ampere \: is \: the \: unit \: of \: current \: electricity}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: Young's \: modulus \: of \: elasticity \: is \: Newton/m^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: pressure \: is \: Pascal}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Curie \: is \: the \: unit \: of \: radio \: activity}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Decibel \: is \: the \: unit \: of \: intensity \: of \: sound}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: electric \: charge \: is \: coulomb}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: resistance \: is \: ohm}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: acceleration \: is \: ms^{-2}}}}$