Why are porcelain objects wrapped in paper or straw before packing for transportation?
Porcelain object are wrapped in paper or straw before packing to reduce the chances of damage during transportation. During transportation sudden jerks or even fall takes place, the force takes longer time to reach the porcelain objects through paper or straw for same change in momentum as $$F=\frac{\Delta p}{\Delta t}$$ and therefore, a lesser force acts on object.
Why does a child feel more pain when she falls down on a hard cement floor, than when she falls on the soft muddy ground in the garden?
When a child falls on a cement floor, her body comes to rest instantly. But $$F \times \Delta t=$$ change in momentum $$=$$ constant. As time of stopping $$\Delta t$$ decreases, therefore $$F$$ increases and hence, child feel more pain.
When she falls on a soft muddy ground in the garden the time of stopping increases and hence, $$F$$ decreases and she feels lesser pain.
A woman throws an object of mass 500 g with a speed of $$25 \mathrm{~ms}^{-1}$$.
(a) What is the impulse imparted to the object?
(b) If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object?
Mass of the object $$(m)=500 \mathrm{~g}=0.5 \mathrm{~kg}$$
Speed of the object $$(v)=25 \mathrm{~m} / \mathrm{s}$$
(a) Impulse imparted to the object = change in momentum
$$\begin{aligned} & =m v-m u \\ & =m(v-u) \\ & =0.5(25-0)=12.5 \mathrm{~N}-\mathrm{s} \end{aligned}$$
(b) Velocity of the object after rebounding
$$\begin{aligned} & =-\frac{25}{2} \mathrm{~m} / \mathrm{s} \\ v^{\prime} & =-12.5 \mathrm{~m} / \mathrm{s} \\ \therefore \quad \text { Change in momentum } & =m\left(v^{\prime}-v\right) \\ & =0.5(-12.5-25)=-18.75 \mathrm{~N}-\mathrm{s} \end{aligned}$$
Why are mountain roads generally made winding upwards rather than going straight up?
While going up a mountain, the force of friction acting on a vehicle of mass $$m$$ is $$f=\mu R=\mu \mathrm{mg} \cos \theta$$, where $$\theta$$ is the angle of slope of the road with the horizontal. To avoid skidding force of friction ($$f$$) should be large and therefore, $$\cos \theta$$ should be large and hence, $$\theta$$ should be small.
That's why mountain roads are generally made winding upwards rather than going straight upto avoid skidding.
A mass of 2 kg is suspended with thread $$A B$$ (figure). Thread $$C D$$ of the same type is attached to the other end of 2 kg mass. Lower thread is pulled gradually, harder and harder in the downward direction, so as to apply force on $$A B$$. Which of the threads will break and why?
The thread $$A B$$ will break earlier than the thread $$C D$$. This is because force acting on thread $$C D=$$ applied force and force acting on thread $$A B=$$ (applied force + weight of 2 kg mass). Hence, force acting on thread $$A B$$ is larger than the force acting on thread $$C D$$.