Λtrolley of mass 100 kg, starting from rest, describes 100 m in 10 second. that instant, i.e.,

step 1 So let's solve this question. So in this question we have this question we have s equals to Ut p

Λtrolley of mass 100 kg, starting from rest, describes 100...

$\Lambda$ trolley of mass $100 \mathrm{~kg}$, starting from rest, describes $100 \mathrm{~m}$ in 10 second. \Lambdat that instant, i.e., at the commencement of the $11^{\text {th }}$ second, two packets, each of mass $12.5 \mathrm{~kg}$, are gently placed in the trolley. I low far does it move in the next 10 seconds assuming that the forces on the trolley remain the same throughout? Solution Since $s-u t+\frac{1}{2} a t^{2}$ $100-0 \div \frac{1}{2} a 100 \quad \therefore \quad a-2 \mathrm{~m} / \mathrm{sec}^{2}$ The velocity at the cnd of 10 seconds $=v=u+a t=0+2 \times 10=20 \mathrm{~m} / \mathrm{s}$ $F=m a=100 \times 2=200 \mathrm{~N}$ During the next 10 seconds, acceleration $-\frac{200}{125}-1.6 \mathrm{~m} / \mathrm{sec}^{2}$ The velocity al the commenecment of the 11 th socond $v^{\prime}$ is given by $m u=m^{\prime} v^{\prime}$ (Taw of conscrvation of momentum) $100 \times 20=125 \times v^{\prime}$ $\therefore \quad v^{\prime}-\frac{100 \times 20}{125}-16 \mathrm{~m} / \mathrm{scc}$ $\therefore$ The distance travelled in the next 10 seconds $=s^{\prime}-u t+\frac{1}{2} a t^{2}$ $-16 \times 10+\frac{1}{2} \times 1.6 \times 100-240 \mathrm{~m}$

$\Lambda$ trolley of mass $100 \mathrm{~kg}$, starting from rest, describes $100 \mathrm{~m}$ in 10 second. \Lambdat that instant, i.e., at the commencement of the $11^{\text {th }}$ second, two packets, each of mass $12.5 \mathrm{~kg}$, are gently placed in the trolley. I low far does it move in the next 10 seconds assuming that the forces on the trolley remain the same throughout? Solution Since $s-u t+\frac{1}{2} a t^{2}$
$100-0 \div \frac{1}{2} a 100 \quad \therefore \quad a-2 \mathrm{~m} / \mathrm{sec}^{2}$
The velocity at the cnd of 10 seconds $=v=u+a t=0+2 \times 10=20 \mathrm{~m} / \mathrm{s}$ $F=m a=100 \times 2=200 \mathrm{~N}$
During the next 10 seconds, acceleration $-\frac{200}{125}-1.6 \mathrm{~m} / \mathrm{sec}^{2}$ The velocity al the commenecment of the 11 th socond $v^{\prime}$ is given by $m u=m^{\prime} v^{\prime}$ (Taw of conscrvation of momentum) $100 \times 20=125 \times v^{\prime}$
$\therefore \quad v^{\prime}-\frac{100 \times 20}{125}-16 \mathrm{~m} / \mathrm{scc}$
$\therefore$ The distance travelled in the next 10 seconds $=s^{\prime}-u t+\frac{1}{2} a t^{2}$ $-16 \times 10+\frac{1}{2} \times 1.6 \times 100-240 \mathrm{~m}$

Key Concepts

Impact of Mass Variation on Dynamics

Altering the mass of a system while maintaining the same net external force leads to a change in the acceleration of the system. As acceleration depends inversely on mass (a = F/m), an increase in mass under a constant force results in a lower acceleration. This concept is crucial when analyzing systems where mass is not constant, allowing predictions of subsequent motion.

Conservation of Linear Momentum

When additional mass is added to a moving system in such a way that no external impulsive forces are introduced, the total linear momentum of the system is conserved. This principle is used to determine the new velocity of the system after mass is changed, by equating the momentum before and after the mass addition.

Newton's Second Law

Newton's Second Law establishes the relationship between the net force acting on an object, its mass, and the resulting acceleration (F = ma). This law is foundational in dynamics as it provides a direct link between how forces affect the motion of an object and is used to determine unknown variables when the mass and force are known.

Uniformly Accelerated Motion

This concept deals with the motion in which the velocity of an object changes at a constant rate. The basic kinematic equations, such as s = ut + 1/2 at², are used to relate displacement, initial velocity, acceleration, and time. Understanding uniformly accelerated motion is essential for problems where an object starts from rest or has a steady change in velocity under constant forces.

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