302 - Mechanics part 1 Questions Answers

Use formula F(min)/mg = mg/F(max)

Now solve. Watch this video

$$\begin{gathered} Impulse is \overrightarrow{Ft} and Power = W/t \\ \overrightarrow{F}=m\overrightarrow{g} and W = mgh \\ Now calculate the time of motion \\ and get the answer \end{gathered}$$

No horizontal force.

Draw a perpendicular from centre to horizontal plane. Then calculate horizontal distance. 

Now solve. 

If any problem, then inform

$$\begin{gathered} According to given condition \\ \frac{d\theta }{dt}=\frac{v\sin 60}{a-(v+v\cos 60)t} \\ Now solve it for t \\ then dis\tan ce = vt \end{gathered}$$solve 

inform for any difficulty

At the front of the cylinder, see a tilted circle $$\begin{gathered} Now compare this problem with vertical circular motion. \\ A is the top point of that path. We know that the \\ minimum velocity at top point \tan gential to path of \\ vertical circle should be \sqrt{gr}. \\ Here due to tilt of this circle effective gravity = g\cos \alpha \\ so v\sin \phi =\sqrt{g\cos \alpha r} \\ now solve \\ inform for any issue \\ wait for video \end{gathered}$$

According to first given condition velocity component of rain = u

let vertical component of rain = v

According to second condition 

velocity of rain relative to man 

$=(nu-u)(-\hat{i})+v(-\hat{j})$$$\begin{gathered} here direction of motion of man is \hat{i} and \\ vertically upward direction is considered as \hat{j} \\ Now draw triangle for this vector and get cot\theta \\ solve it \\ inform for any issue \end{gathered}$$

Updated:

Initially there is no external force. Centre of mass of the system accelerates when insect moves with acceleration.

Now suppose displacement of insect at t = t is x with respect to rod, and y is the acceleration of rod in downward direction with respect to ground. Thus acceleration of counterweight is y with respect to ground. Now$\overrightarrow{x_{CM}}=\left[m\right(x-y)\hat{j}-(M-m)y\hat{j}+My\hat{j}]/2M$Now solve for x = l,

For dynamics, take friction upward in free body diagram of insect and downward in the free body diagram of rod.

Now solve

Inform for any issue.