(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

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$A$ 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

$A$ rigid body of mass $4 \ kg$ initially at rest moves under the action of an applied horizontal force of $18 \ N$ on a table with a coefficient of kinetic friction of $0.2$. The work done by the applied force on the body in $10 \ s$ will be $.... \ J$.

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Two identical blocks $A$ and $B$,each of mass $m$,resting on a smooth horizontal floor,are connected by a light spring of natural length $L$ and spring constant $K$. $A$ third block $C$ of mass $m$,moving with a speed $v$ along the line joining $A$ and $B$,collides with $A$. The maximum compression in the spring is:

DifficultJEE MAIN 2021

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Two wooden blocks of mass $M_1$ and $M_2$ rest on a frictionless table. $A$ bullet of mass $m$ is fired at $M_1$ with speed $v$,which gets embedded in it,and the two together finally collide with $M_2$. Find the velocity of $M_2$ after the collision. (Assume the collision between the $(M_1+m)$ system and $M_2$ is elastic and treat the problem as one-dimensional.)

EasyAP EAMCET 2022

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$A$ $0.5\, kg$ ball is thrown up with an initial speed $14\, m/s$ and reaches a maximum height of $8.0\, m$. How much energy is dissipated by air drag acting on the ball during the ascent? (Take $g = 9.8\, m/s^2$)

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$A$ ball is thrown from $10 \, m$ height at speed $v_0$ vertically downward. Upon colliding with the surface of the earth,it loses $50 \%$ of its energy and again reaches the same height. The value of $v_0$ is: ................. $m/s$

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$A$ rigid body of mass $4 \ kg$ initially at rest moves under the action of an applied horizontal force of $18 \ N$ on a table with a coefficient of kinetic friction of $0.2$. The work done by the applied force on the body in $10 \ s$ will be $.... \ J$.

$A$ $0.5\, kg$ ball is thrown up with an initial speed $14\, m/s$ and reaches a maximum height of $8.0\, m$. How much energy is dissipated by air drag acting on the ball during the ascent? (Take $g = 9.8\, m/s^2$)

$A$ ball is thrown from $10 \, m$ height at speed $v_0$ vertically downward. Upon colliding with the surface of the earth,it loses $50 \%$ of its energy and again reaches the same height. The value of $v_0$ is: ................. $m/s$

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