A particle moves from a point r 1 → = 2 m i ^ + 3 m j ^ to the another point r 2 → = 3 m i ^ + 2 m j ^ during which a certain force F → = 5 i ^ + 5 j ^ N acts on it. Find the work done by the force, on the particle during the displacement.

The initial position vector, r 1 → = 2 i ^ + 3 j ^ m . The final position vector, r 2 → = 3 i ^ + 2 j ^ m . So, the displacement vector, r → = r 2 → - r 1 → = 3 i ^ + 2 j ^ - 2 i ^ + 3 j ^ = i ^ - j ^ m The force acting on the particle, F → = 5 i ^ + 5 j ^ N So, the work done = F → · s → = 5 i ^ + 5 j ^ · i ^ - j ^ = 5 × 1 + 5 - 1 = 0 The work done by the force acting on the particle is 0 J .

A particle being acted on by constant forces 4 i ^ + j ^ - 3 k ^ and 3 i ^ + j ^ - k ^ is displaced from the point i ^ + 2 j ^ - 3 k ^ to the point 5 i ^ + 4 j ^ - k ^ . Find the total work done by the forces.

The work done by the force is found by multiplying the resultant of the forces and the displacement vector, W = R → · d → . Let the constant forces be A → = 4 i ^ + j ^ - 3 k ^ and B → = 3 i ^ + j ^ - k ^ , then their resultant is obtained as R → = A → + B → . = 4 i ^ + j ^ - 3 k ^ + 3 i ^ + j ^ - k ^ = 7 i ^ + 2 j ^ - 4 k ^ Let the particle be displaced from point C to D having position vectors as O C → = i ^ + 2 j ^ - 3 k ^ and O D → = 5 i ^ + 4 j ^ - k ^ , then the displacement vector is given by d → = O D → - O C → = 5 i ^ + 4 j ^ - k ^ - i ^ + 2 j ^ - 3 k ^ = 4 i ^ + 2 j ^ + 2 k ^ Therefore, the work done is obtained as W = R → · d → . ⇒ W = 7 i ^ + 2 j ^ - 4 k ^ · 4 i ^ + 2 j ^ + 2 k ^ ⇒ W = 7 × 4 + 2 × 2 + - 4 × + 2 ⇒ W = 28 + 4 - 8 ∴ W = 24 units

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A chain is kept on a frictionless table with one fourth of its length hanging over the edge. If the chain has length $l$ and a mass $m$ , how much work is required to pull the hanging part back on the table?

Important Questions on Work, Energy and Power

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 10

A block of mass

250 g

is kept on a vertical spring of spring constant

100 N m^{- 1}

fixed from below. The spring is now compressed to have a length

10 cm

shorter than its natural length and the system is released from this position. How high does the block rise? Take

g = 10 m s^{- 2}

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 11

A block of mass

m

is suspended by a spring of spring constant

k

and is in equilibrium. A sharp blow gives the block an initial downward velocity

v

. How far below the equilibrium position, the block comes to rest for a moment?

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 12

The effective length of a pendulum is

50 cm

and the mass of its bob is

4 g

. The bob is drawn to a slide till the string is horizontal and then released. Find the kinetic energy when the string makes an angle of

60 °

with the vertical.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 13

The pump of a fire engine lifts

50 kg

of water per second from a reservoir

2.5 m

below ground level. The water hits a wall

7.5 m

high with a speed of

5 {ms}^{- 1}

. Find the power of the engine in H.P (.

g = 9.8 {ms}^{- 2}; 1 H . P . = 746

watt.)

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 14

A block of mass $M$ is attached to two unstretched light springs of spring constants $k_{1}$ and $k_{2}$ as shown in figure below. The block is displaced towards right through a distance $x$ and is released. Find the speed of the block as it passes through the mean position.

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 15

A particle moves from a point

\vec{r_{1}} = (2 m) \hat{i} + (3 m) \hat{j}

to the another point

\vec{r_{2}} = (3 m) \hat{i} + (2 m) \hat{j}

during which a certain force

\vec{F} = (5 \hat{i} + 5 \hat{j}) N

acts on it. Find the work done by the force, on the particle during the displacement.

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 16

A particle being acted on by constant forces

(4 \hat{i} + \hat{j} - 3 \hat{k})

and

(3 \hat{i} + \hat{j} - \hat{k})

is displaced from the point

(\hat{i} + 2 \hat{j} - 3 \hat{k})

to the point

(5 \hat{i} + 4 \hat{j} - \hat{k})

. Find the total work done by the forces.

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11th West Bengal Board

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A Text Book of PHYSICS PART I : CLASS 11>Chapter 9 - Work, Energy and Power>EXERCISE>Q 17

A $0.5 kg$ body slides from the point $A$ , figure along a horizontal track with an initial speed of $3 {ms}^{- 1}$ towards a weightless horizontal spring of length $1 m$ and force constant $2 {Nm}^{- 1}$ . The part $A B$ of the track is frictionless and the part $B C$ has the coefficient of static and dynamic friction $0.22$ and $0.2$ respectively. Find the total distance through which the block moves before it comes to rest completely $(g = 10 m / s^{2})$ , if $A B = 2 m$ and $B D = 2.14 m$ .

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A chain is kept on a frictionless table with one fourth of its length hanging over the edge. If the chain has length l and a mass m, how much work is required to pull the hanging part back on the table?

Important Questions on Work, Energy and Power

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A chain is kept on a frictionless table with one fourth of its length hanging over the edge. If the chain has length $l$ and a mass $m$ , how much work is required to pull the hanging part back on the table?