Newton's laws of motion
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1
F when m is constant and when v is constant
F=ma (m is constant) F=v*dm/dt (v is constant)
2
impulse
I=F∆t =∆p
3
rocket propulsion
Fnet=udm/dt-mg
4
recoil of gun
MV=-mv
5
collision (impulse general case , perfectly elastic, oblique)
impulse general case I=m(v1+v2) perfectly elastic I=2mv oblique elastic collision I=2mvcos(theta)
6
bullet plate when equilibrium equation
2mnv=Mg where n is no of bullets strikes in ∆t time
7
spring force F=-kx
8
lift problem (when accelerating upwards ,downwards, moving with constant velocity(or rest ), wapp =?
lift is rest of constant velocity wapp=mg accelerating upwards wapp=m(g+a) accelerating down wards = m(g-a)
9
minimum time to climb l length rope
tmin=√(2l/amax)
10
T at point on rope due to force F x is distance from one end end which is force applied and to the the desired point to calculate the tension
T=(L-x/L)*F
11
lami's theorem
F1/sin(alpha)=F2/sin(beta)=F3/sin(gamma)
12
pulley system acceleration and tension
a=(m1-m2/m1+m2)g. T=(2m1m2/m1+m2)g
13
spring for different acceleration of blocks
F1-F2=M1a1+M2a2
14
relative slipping (minimum force so that m mass doesn't slip inclined plane having mass M also find acceleration)
F=(m+M)g tan(theta) a=g tan(theta)
15
no relative slipping (a block with mass M is being pushed with a acceleration a mass m2 is on M and m1 Is attached to m2 and hanging through a pulley ) find accleration
a=(m1/m2)g
16
no relative slipping (a wedge is of mass M carrying a mass m on the wedge is connected by pulley to a mass M° then M° should be such that there is no slipping b/w wedge and mass m
M°=(M+m)/(cot(theta)-1)
17
accleration of ball in lift wrt to man in lift (lift is moving upwards with accleration a)
arel=(g+a) T=√(2l+a)
18
accleration of ball in lift wrt to man outside the lift (lift is moving upwards with accleration a)
a=g
19
man cage problem (Tension and Normal force N
T=(m+M)g/2 ,N=(m-M)g/2
20
horizontal truck accleration for box not slipping
a=coefficient of staticfriction*g
21
vertical truck accleration for box not slipping
a=g/coefficient of staticfriction
22
motion of a car on banked road
Vmax=√(coeffient of staticfriction*R*g)
23
banked road
Vmax =√(Rg(tan(theta)+coefficient of staticfriction)/1-coefficientofstaticfriction*tan(theta)
24
voptimum(banked road without friction)=?
√(Rgtan(theta))
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