The position-time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
Given, mass of the body $$(m)=2 \mathrm{~kg}$$
From the position-time graph, the body is at $$x=0$$ when $$t=0$$, i.e., body is at rest.
$$\therefore$$ Impulse at $$t=0, s=0$$, is zero
From $$t=0 \mathrm{~s}$$ to $$t=4 \mathrm{~s}$$, the position-time graph is a straight line, which shows that body moves with uniform velocity.
Beyond $$t=4 \mathrm{~s}$$, the graph is a straight line parallel to time axis, i.e., body is at rest $$(v=0)$$.
Velocity of the body = slope of position-time graph
$$=\tan \theta=\frac{3}{4} \mathrm{~m} / \mathrm{s}$$
Impulse (at $$t=4 \mathrm{~s})=$$ change in momentum
$$\begin{aligned} & =m v-m u \\ & =m(v-u) \\ & =2\left(0-\frac{3}{4}\right) \\ & =-\frac{3}{2} \mathrm{~kg}-\mathrm{m} / \mathrm{s}=-1.5 \mathrm{~kg}-\mathrm{m} / \mathrm{s} \end{aligned}$$
A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing seat belt, he falls forward and hits his head against the steering wheel. Why?
When a person driving a car suddenly applies the brakes, the lower part of the body slower down with the car while upper part of the body continues to move forward due to inertia of motion.
If driver is not wearing seat belt, then he falls forward and his head hit against the steering wheel.
The velocity of a body of mass 2 kg as a function of $$t$$ is given by $$\mathbf{v}(t)=2 t \hat{\mathbf{i}}+t^2 \hat{\mathbf{j}}$$. Find the momentum and the force acting on it, at time $$t=2 \mathrm{~s}$$.
Given, mass of the body $,$m=2 \mathrm{~kg}$$.
Velocity of the body $$\mathbf{v}(t)=2 t \hat{\mathbf{i}}+t^2 \hat{\mathbf{j}}$$
$$\therefore$$ Velocity of the body at $$t=2 \mathrm{~s}$$
$$\mathbf{v}=2 \times 2 \hat{\mathbf{i}}+(2)^2 \hat{\mathbf{j}}=(4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}})$$
Momentum of the body $$(p)=m \mathbf{v}$$
$$=2(4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}})=(8 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}) \mathrm{kg}-\mathrm{m} / \mathrm{s}$$
$$\begin{aligned} \text { Acceleration of the body }(a)=\frac{d \mathbf{v}}{d t} & \\ & =\frac{d}{d t}\left(2 t \hat{\mathbf{i}}+t^2 \hat{\mathbf{j}}\right) \\ & =(2 \hat{\mathbf{i}}+2 t \hat{\mathbf{j}}) \\ \text { At } t & =2 s \\ \mathbf{a} & =(2 \hat{\mathbf{i}}+2 \times 2 \hat{\mathbf{j}}) \\ & =(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \end{aligned}$$
$$\begin{aligned} & \text { Force acting on the body }(\mathbf{F})=m \mathbf{a} \\ & \qquad \begin{aligned} & =2(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \\ & =(4 \hat{\mathbf{i}}+8 \hat{\mathbf{j}}) \mathrm{N} \end{aligned} \end{aligned}$$
A block placed on a rough horizontal surface is pulled by a horizontal force $$F$$. Let $$f$$ be the force applied by the rough surface on the block. Plot a graph of $$f$$ versus $$F$$.
The approximate graph is shown in the diagram
The frictional force $$f$$ is shown on vertical axis and the applied force $$F$$ is shown on the horizontal axis. The portion OA of graph represents static friction which is self adjusting. In this portion, $$f=F$$.
The point $$B$$ corresponds to force of limiting friction which is the maximum value of static friction. $$C D \| O X$$ represents kinetic friction, when the body actually starts moving. The force of kinetic friction does not increase with applied force, and is slightly less than limiting friction.
Why are porcelain objects wrapped in paper or straw before packing for transportation?
Porcelain object are wrapped in paper or straw before packing to reduce the chances of damage during transportation. During transportation sudden jerks or even fall takes place, the force takes longer time to reach the porcelain objects through paper or straw for same change in momentum as $$F=\frac{\Delta p}{\Delta t}$$ and therefore, a lesser force acts on object.