Advertisements
Advertisements
Question
Suppose the ceiling in the previous problem is that of an elevator which is going up with an acceleration of 2.0 m/s2. Find the elongation.
Advertisements
Solution
When the ceiling of the elevator is going up with an acceleration 'a', then a pseudo-force acts on the block in the downward direction.
a = 2 m/s2
From the free-body diagram of the block,
kx = mg + ma
⇒ kx = 2g + 2a
= 2 × 9.8 + 2 × 2
= 19.6 + 4
\[\Rightarrow x = \frac{23 . 6}{100} = 0 . 236 \approx 0 . 24 \text{ m }\]
When 1 kg body is added,
total mass = (2 + 1) kg = 3 kg
Let elongation be x'.
∴ kx' = 3g + 3a = 3 × 9.8 + 6
\[ = 0 . 354 \approx 0 . 36 m\]
So, further elongation = x' − x
= 0.36 − 0.24 = 0.12 m.
APPEARS IN
RELATED QUESTIONS
A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m s–2. Calculate the initial thrust (force) of the blast.
The below figure shows the position-time graph of a particle of mass 4 kg.
- What is the force on the particle for t < 0, t > 4 s, 0 < t < 4 s?
- What is the impulse at t = 0 and t = 4 s? (Consider one-dimensional motion only.)
A batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of the ball is 0.15 kg.)
A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block has a magnitude.
A person is standing on a weighing machine placed on the floor of an elevator. The elevator starts going up with some acceleration, moves with uniform velocity for a while and finally decelerates to stop. The maximum and the minimum weights recorded are 72 kg and 60 kg, respectively. Assuming that the magnitudes of acceleration and deceleration are the same, find (a) the true weight of the person and (b) the magnitude of the acceleration. Take g = 9.9 m/s2.
In the previous problem, suppose m2 = 2.0 kg and m3 = 3.0 kg. What should be the mass m, so that it remains at rest?
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.
A monkey of mass 15 kg is climbing a rope fixed to a ceiling. If it wishes to go up with an acceleration of 1 m/s2, how much force should it apply on the rope? If the rope is 5 m long and the monkey starts from rest, how much time will it take to reach the ceiling?
In the following figure shows a man of mass 60 kg standing on a light weighing machine kept in a box of mass 30 kg. The box is hanging from a pulley fixed to the ceiling by a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, what is the weight recorded on the machine? What force should he exert on the rope to record his correct weight on the machine?
A block A can slide on a frictionless incline of angle θ and length l, kept inside an elevator going up with uniform velocity v in the following figure. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.
State the Newton's second law of motion. What information do you get from it?
How can Newton's first law of motion be obtained from the second law of motion?
Use Newton's second law of motion to explain the following instance :
A cricketer pulls his hands back while catching a fast moving cricket ball .
The unit of linear momentum is :
A body of mass 5 kg is moving with velocity 2 m s-1. Calculate its linear momentum.
The linear momentum of a ball of mass 50 g is 0.5 kg m s-1. Find its velocity.
A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g = 10 m s-2 and speed of sound = 330 m s-1. Find : The time when echo is heard after the pebble is dropped.
A stone is dropped from a tower 98 m high. With what speed should a second stone be thrown 1 s later so that both hit the ground at the same time?
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is ______.
Figure shows (x, t), (y, t ) diagram of a particle moving in 2-dimensions.
|
|
 (b) |
If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.
