A man weighing M kg, stands on a weighing machine inside a lift. What will be the reading of the machine if it:
(a) descends with acceleration a,
(b) ascends with an acceleration a and
(c) moves with constant velocity in upward direction?
(a)
The true weight of body = Mg
Reaction of floor = R
Net force acting on the body is,
F = Mg - R
If a is the acceleration with which lift moves downward, then
F = M a
∴ Ma = Mg - R
i.e., R = M(g - a)
Thus the apparent weight of the body is,
(b)
If lift is ascending in upward direction with acceleration a then
Ma = R - Mg
or
(c)
If lift moves with constant velocity then acceleration, a = 0.
∴
So, reading on the machine = Mg
Ans.
(i) For ,
The force acting on the body is constant. Thus, the body has uniform accelerated motion.
(ii) For,
Force on the body is zero, therefore body has uniform motion.
(iii) For ,
The force is negative and increases linearly with time in magnitude, thus the motion is non-uniformly retarded motion.
(iv) For ,
The force is positive and increases linearly with time, thus the motion is non-uniformly accelerated motion.
(v) For ,
The force acting on the body is constant, thus the body has uniform accelerated motion.
(vi) For ,
The force acting on the body is constant and negative, thus the body has uniformly retarded motion.
Law of conservation of momentum:
It states that total momentum of system remains conserved in the absence of external force.
After explosion,
Let 2 kg mass after explosion fly off along X-axis and 3 kg mass fly off along Y-axis perpendicular to direction of motion of 2 kg mass.
Suppose the velocity of third fragment after explosion is
∴ Momentum of 2 kg mass is,
Momentum of 3 kg mass is,
Momentum of 5 kg mass is,
According to the law of conservation of linear momentum,
∴
This is the required velocity of the third fragment.
Second law is the real law of motion. This can be proved by showing that first law and third law are contained in second law of motion.
(i) First law is contained in second law. According to the second law of motion,
That is if no force is acting on the body then its acceleration is zero, means if a body is at rest, it remains at rest and if the body is moving in straight line with constant velocity, it continues to do so. This is what the first law states. Hence first law is contained in the second law.
(ii) Third law is contained in second. According to the second law of motion,