Question

What will be your weight while
travelling in an escalator?(consider
both directions) Will it increase,
decrease or remain the same. Support
your answer with a valid reason.
Pls ans thoroughly

Answer 1

Answer:

To understand:

Effects on weight while travelling in an elevator.

Explaination:

Weight of a body on a surface is actually represented by the normal force acting on it. For example , when you stand on the weighing machine , it records the NORMAL REACTION FORCE.

1st Case (Lift going up):

Let the acceleration of the lift be "a" going upwards. So the object in the lift will experience a pseudo-force downwards.

\therefore \: mg + ma = N∴mg+ma=N

= > \: N = mg + ma=>N=mg+ma

= > \: N > mg=>N>mg

So, the apparent weight of the object will be greater than the actual weight.

2nd Case (Lift going down):

Let the lift go down with the acceleration "a" , such that the object will experience a pseudo force upwards.

\therefore \: mg - ma = N∴mg−ma=N

= > \: N = mg - ma=>N=mg−ma

= > \: N < mg=>N<mg

So, the apparent weight is lesser than the actual weight of the object.

Hence, when the lift undergoes free fall (accelerated downwards with "g" ) , the normal reaction becomes zero and the object feels weightless.

I Hope It Helps you

Answer 2

Question 1 on Escalator based problems: Anand takes 90 secs to move up an escalator which is moving downward and he takes 30 secs to move down the same escalator. How much time will he take to go up or down, when the escalator is switched off?

Solution:

Method 1-

Take the length of the stairs LCM(90,30) = 90

Time taken when going upstream is 90 sec, so we can say

M – E = 90/90 = 1

M + E = 90/30 = 3

So speed of Man = 4/2 = 2

Time taken is 90/2 = 45 sec

Method 2 – Shortcut

When moving upstream speed is M + E

when moving when escalator is stopped is M

and when moving upstream speed is M – E

speed is in AP, so time will be in HP, since they are inversely proportional.

So time taken would be –

2 x 90 x 30 / (90+30) = 60 x 90/120 = 45 secs

Case B: Where the number of steps are asked

Question 2 on Escalator based problems: When Ramu walks down, he takes 1 minute on an escalator which is moving down but takes 40 seconds when he runs down. He takes 20 steps when he is walking whereas he takes 30 steps when he is running. Calculate the total number of steps in the escalator?

Solution:

Assume the speed of the escalator to be “a” steps per second.

As it is an escalator, distance covered by Ramu will always be same whether he is running or walking.

Case 1:

Distance when Ramu is walking = 20 + 60a Eq. 1

Here, 60a is covered by the escalator.

Case 2:

Distance when Ramu is running = 30 + 40a Eq. 2

Again, 40a is the distance covered by the escalator.

Now, equating both the equations, obtained equation is:

20 + 60a = 30 + 40a

=> a = 0.5

So, total number of steps will be = 20 + 60 (0.5) = 50 steps.

Type 2: Two people are moving on escalator

Case A: When both people are moving in same direction

Question 3 on Escalator based problems: P and Q walk up a moving up escalator at constant speeds. For every 5 steps that P takes Q takes 3 steps. How many steps would each have to climb when the escalator is switched off, given that P takes 50 and Q takes 40 steps to climb up the moving up escalator respectively?

Solution:

Both the person and the escalator are moving in the same direction. In this case, the relative speed would be Speed of (Man + Stairs)

We don’t know the speed of the escalator, so assume that to be E

Now think, both for P and Q the length of the escalator should be same, right?

and P speed is 5 steps/sec (say) and Q’s is 3 steps/sec

P is walking 50 steps and he does it in 10 sec..but in this 10 sec, even the escalator must have moved with speed “E”. The length moved by it would be 10E

So we can say the total length is 50 + 10 E ( step moved by P and the escalator helps P in reaching the top.

Similarly for Q we can write 40 + 40/3 * E

Both lengths must be same, so –

50 + 10 E = 40 + 40E/3

So E = 3

So total length is 50 + 10 E = 80

Case B: When both people are moving in opposite directions

Question 4 on Escalator based problems::A can take 10 steps per second and B can take 7 steps per second. A mischievously starts climbing down an escalator that is moving upwards and at the same instant B starts climbing up the same escalator. They meet after 5 seconds. If the escalator works at a steady rate of 4 steps per second then how many steps are visible when the escalator is stopped?

Sol:

A and B take 10 and 7 steps per second. Escalator takes 4 steps per second.

A is climbing down so effective speed is 10 – 4 =6 steps/sec

B is climbing up so effective speed is 7 + 4 = 11 steps/sec

They are moving in opp directions so rel speed is 17 steps/sec.

As they meet in 5 sec, total steps = 17 * 5 = 85 steps.