(C) To move the particle slowly,the external force must overcome both gravity and friction.Work done $W = W_{\text{gravity}} + W_{\text{friction}}$.Si

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(C) To move the particle slowly,the external force must overcome both gravity and friction.Work done $W = W_{\text{gravity}} + W_{\text{friction}}$.Since the particle starts and ends at the same height (assuming $A$ and $E$ are at ground level,$h_A = h_E = 0$),the net work done against gravity is $mgh_E - mgh_A = 0$.Work done against friction is $W_f = \int \mu N \ ds = \mu \int mg \cos \theta \ ds = \mu mg \int \cos \theta \ ds$.Since $\int \cos \theta \ ds$ represents the horizontal displacement,we have $\int \cos \theta \ ds = AE = 10 \ m$.Therefore,$W_f = \mu mg (AE) = 0.6 \times 3 \times 10 \times 10 = 180 \ J$.Total work done $W = 0 + 180 = 180 \ J$.

Class 11 Physics Work, Energy, Power and Collision Mix Examples-Work, Energy, Power and Collision

Difficult

$A$ particle of mass $3 \ kg$ is moved slowly along the path $ABCDE$ from $A$ to $E$. The heights of $B$,$C$,and $D$ are $5 \ m$,$4 \ m$,and $6 \ m$ respectively. The total path length is $20 \ m$,the horizontal distance $AE = 10 \ m$,and the coefficient of friction $\mu = 0.6$. Calculate the work done in $J$ to slowly move the mass from $A$ to $E$. (Take $g = 10 \ m/s^2$)

A
$360$
B
$200$
C
$180$
D
$400$

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Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

$A$ mass of $1 \; kg$ collides elastically with a stationary mass of $5 \; kg$. After the collision,the $1 \; kg$ mass moves in the opposite direction with a velocity of $2 \; ms^{-1}$. Which of the following statements is correct for this system of two masses?

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$A$ pendulum of length $1 \,m$ and having a bob of mass $1 \,g$ is pulled aside through an angle $60^{\circ}$ with the vertical and then released. The power delivered by all the forces acting on the bob when the pendulum makes $30^{\circ}$ with the vertical is . . . . . . $\left(g=10 \,ms^{-2}\right)$ (in $\,mW$)

MediumAP EAMCET 2017

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$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

DifficultJEE MAIN 2015

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State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.

Medium

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$A$ machine with efficiency $2/3$ uses $12 \text{ J}$ of energy to lift a $2 \text{ kg}$ block to a certain height. If the block is allowed to fall freely from that height,what is its velocity when it reaches the ground?

MediumAP EAMCET 2024

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$A$ mass of $1 \; kg$ collides elastically with a stationary mass of $5 \; kg$. After the collision,the $1 \; kg$ mass moves in the opposite direction with a velocity of $2 \; ms^{-1}$. Which of the following statements is correct for this system of two masses?

$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

State whether the following statements are true or false:$(a)$ Power is the vector product of force and velocity.$(b)$ $1\,kg\,m = 9.8\,J$$(c)$ When a teacher rubs a blackboard with a duster,they do no work.$(d)$ Kinetic energy can be negative.

$A$ machine with efficiency $2/3$ uses $12 \text{ J}$ of energy to lift a $2 \text{ kg}$ block to a certain height. If the block is allowed to fall freely from that height,what is its velocity when it reaches the ground?

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State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.