(D) The work-energy theorem states that the work done by the braking force $F$ is equal to the change in kinetic energy: $W = \Delta K$. Since the fin

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(D) The work-energy theorem states that the work done by the braking force $F$ is equal to the change in kinetic energy: $W = \Delta K$. Since the final velocity is $0$, the work done by the braking force is $F \cdot S = \frac{1}{2} m v^2$. Thus, the stopping distance $S = \frac{m v^2}{2 F}$. Since $v$ and $F$ are constant, $S \propto m$. In the first case, the total mass $m_1 = 80 \ kg + 100 \ kg = 180 \ kg$. So, $S_1 = \frac{180 v^2}{2 F}$. In the second case, the total mass $m_2 = 80 \ kg + 100 \ kg + 60 \ kg = 240 \ kg$. So, $S_2 = \frac{240 v^2}{2 F}$. Taking the ratio: $\frac{S_1}{S_2} = \frac{180}{240} = \frac{3}{4}$. Therefore, $4 S_1 = 3 S_2$.

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

Medium

$A$ man of mass $80 \ kg$ goes to the market on a scooter of mass $100 \ kg$ with a certain speed. On application of brakes, the stopping distance is $S_1$. The man returns home on the same scooter, with the same speed with a $60 \ kg$ bag of rice. If $S_2$ is the new stopping distance when the brakes are applied with the same force, then:

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A
$7 S_1 = 4 S_2$
B
$2 S_1 = S_2$
C
$3 S_1 = 4 S_2$
D
$4 S_1 = 3 S_2$

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Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

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Two blocks of masses $m_1$ and $m_2$ are connected by a spring of spring constant $k$,initially at their natural length as shown. $A$ sharp impulse is given to mass $m_2$ so that it acquires a velocity $v_0$ towards the right. If the system is kept on a smooth floor,find the maximum elongation that the spring will suffer.

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$A$ block of mass $5 \ kg$ is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration $2 \ m/s^2$. The work done by tension on the block during the first $3 \ s$ is $(u = 0)$. (in $J$)

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$A$ small disc of mass $m = 1 \,g$ slides down a smooth hill of height $h = 10 \,cm$ from rest and gets onto a plank of mass $M = 100 \,g$ as shown in the figure. Due to friction between the disc and the plank, the disc slows down and moves as one piece with the plank. The work done by the frictional force is approximately (Use $g = 10 \,m/s^2$): (in $\,J$)

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Consider two carts,of masses $m$ and $2m$,at rest on an air track. If you push both the carts for $3\,s$ exerting equal force on each,the kinetic energy of the light cart is

Medium

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Three objects $A, B$,and $C$ are placed on a frictionless horizontal surface. Their masses are $m, 2m$,and $m$ respectively. Object $A$ moves towards $B$ with a speed of $9 \ m/s$ and undergoes an elastic collision with it. Subsequently,$B$ undergoes a perfectly inelastic collision with $C$. All motion occurs along the same straight line. What will be the final speed of object $C$ in $m/s$?

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$A$ block of mass $5 \ kg$ is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration $2 \ m/s^2$. The work done by tension on the block during the first $3 \ s$ is $(u = 0)$. (in $J$)

Consider two carts,of masses $m$ and $2m$,at rest on an air track. If you push both the carts for $3\,s$ exerting equal force on each,the kinetic energy of the light cart is

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