Advertisements
Advertisements
प्रश्न
A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m s–2. The crew and the passengers weigh 300 kg. Give the magnitude and direction of the
(a) force on the floor by the crew and passengers,
(b) action of the rotor of the helicopter on the surrounding air,
(c) force on the helicopter due to the surrounding air.
Advertisements
उत्तर १
(a) Mass of the helicopter, mh = 1000 kg
Mass of the crew and passengers, mp = 300 kg
Total mass of the system, m = 1300 kg
Acceleration of the helicopter, a = 15 m/s2
Using Newton’s second law of motion, the reaction force R, on the system by the floor can be calculated as:
R – mpg = ma
= mp(g + a)
= 300 (10 + 15) = 300 × 25
= 7500 N
Since the helicopter is accelerating vertically upward, the reaction force will also be directed upward. Therefore, as per Newton’s third law of motion, the force on the floor by the crew and passengers is 7500 N, directed downward.
(b) Using Newton’s second law of motion, the reaction force R’, experienced by the helicopter can be calculated as:
R' - mg = ma
=m(g+a)
=1300(10+15) = 1300 xx 25
= 32500 N
The reaction force experienced by the helicopter from the surrounding air is acting upward. Hence, as per Newton’s third law of motion, the action of the rotor on the surrounding air will be 32500 N, directed downward.
(c) The force on the helicopter due to the surrounding air is 32500 N, directed upward.
उत्तर २
Here, mass of helicopter, m1= 1000 kg
Mass of the crew and passengers, m2 = 300 kg upward acceleration, a = 15 ms-2and g = 10 ms-2
(a)Force on the floor of helicopter by the crew and passengers = apparent weight of crew and passengers
= m2 (g + a) = 300 (10 + 15) N = 7500 N
(b)Action of rotor of helicopter on surrounding air is obviously vertically downwards, because helicopter rises on account of reaction to this force. Thus, force of action
F = (m1+ m2) (g + a) = (1000 + 300) (10 + 15) = 1300 x 25 = 32500 N
(c)Force on the helicopter due to surrounding air is the reaction. As action and reaction are equal and opposite, therefore, force of reaction, F = 32500 N, vertically upwards.
संबंधित प्रश्न
A man of mass 70 kg stands on a weighing scale in a lift which is moving
- upwards with a uniform speed of 10 m s-1
- downwards with a uniform acceleration of 5 m s–2
- upwards with a uniform acceleration of 5 m s–2. What would be the readings on the scale in each case?
- What would be the reading if the lift mechanism failed and it hurtled down freely under gravity?
The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s–2. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).
You are travelling in a car. The driver suddenly applies the brakes and you are pushed forward. Why does this happen?
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will.
An empty plastic box of mass m is found to accelerate up at the rate of g/6 when placed deep inside water. How much sand should be put inside the box so that it may accelerate down at the rate of g/6?
Consider the situation shown in the following figure. Both the pulleys and the string are light and all the surfaces are frictionless.
- Find the acceleration of the mass M.
- Find the tension in the string.
- Calculate the force exerted by the clamp on the pulley A in the figure.
Find the acceleration of the blocks A and B in the three situations shown in the following figure.
The monkey B, shown in the following figure, is holding on to the tail of monkey A that is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg, respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry monkey B with it? Take g = 10 m/s2.
A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/s2. Find the displacement of the block during the first 0.2 s after the start. Take g = 10 m/s2.
Two bodies A and B of same mass are moving with velocities v and 2v, respectively. Compare their (i) inertia and (ii) momentum.
The correct form of Newton's second law is :
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : Change in momentum of the body.
How long will a stone take to fall to the ground from the top of a building 80 m high
An electron of mass 9 × 10−31 kg is moving with a linear velocity of 6 × 107 ms−1. Calculate the linear momentum of electron.
A motorcycle of mass 100 kg is running at 10 ms−1. If its engine develops an extra linear momentum of 2000 Ns, calculate the new velocity of a motorcycle.
What do you understand by the term momentum?
A stone is dropped from a cliff 98 m high.
How long will it take to fall to the foot of the cliff?
In the previous problem (5.3), the magnitude of the momentum transferred during the hit is ______.
