Advertisements
Advertisements
प्रश्न
A body of mass 0.40 kg moving initially with a constant speed of 10 m s–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.
Advertisements
उत्तर
Mass of the body, m = 0.40 kg
Initial speed of the body, u = 10 m/s due north
Force acting on the body, F = -8.0 N
Acceleration produced in the body, `a = "F"/"m" = (-8.0)/(0.40) = -20 "m/s"^2`
(i) At t = -5s
Acceleration, a' = 0 and u = 10 m/s
`"S" = "ut" + 1/2 "at"^2`
= 10 × (-5) = -50 m
(ii) At t = 25 s
Acceleration, a'' = -20 m/s2 and u = 10 m/s
S = ut + `1/2` at2
`= 10 xx 25 + 1/2 xx (-20) xx (25)^2`
= 250 + 6250 = -6000 m
(iii) At t = 100 s
For `0 <= t <= 30`
a = –20 m/s2
u = 10 m/s
S1 = ut + `1/2` at2
`= 10 xx 30 + 1/2 xx (-20) xx (30)^2`
= 300 - 9000
= -8700 m
For 30' < t <= 100s
As per the first equation of motion, for t = 30 s, final velocity is given as:
v = u + at
= 10 + (-20) × 30 = -590 m/s
Velocity of the body after 30 s = -590 m/s
For motion between 30 s to 100 s, i.e., in 70 s:
S2 = vt
= -590 × 70 = -41300 m
∴ Total distance, S = s1 + s2 = -8700 - 41300 = -50000 m
APPEARS IN
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 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 stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are: [Choose the correct alternative]
| Lowest Point | Highest Point | |
| a) | mg – T1 | mg + T2 |
| b) | mg + T1 | mg – T2 |
| c) | `mg + T1 –(m_v_1^2)/R` | mg – T2 + (`mv_1^2`)/R |
| d) | `mg – T1 – (mv)/R` | mg + T2 + (mv_1^2)/R |
T1 and v1 denote the tension and speed at the lowest point. T2 and v2 denote corresponding values at the highest point.
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.
The figure shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region
(a) AB
(b) BC
(c) CD
(d) DE
Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.
Consider the Atwood machine of the previous problem. The larger mass is stopped for a moment, 2.0 s after the system is set into motion. Find the time that elapses before the string is tight again.
Consider the situation shown in the following figure All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of acceleration of the two blocks.
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?
Find the acceleration of the 500 g block in the following 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?
Two balls A and B of masses m and 2 m are in motion with velocities 2v and v, respectively. Compare:
(i) Their inertia.
(ii) Their momentum.
(iii) The force needed to stop them in the same time.
ame the law of motion which gives the definition of force.
A stone is dropped from a cliff 98 m high.
How long will it take to fall to the foot of the cliff?
Why does a child feel more pain when she falls down on a hard cement floor, than when she falls on the soft muddy ground in the garden?
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.
Why is catching a slow-moving ball easier than catching a fast-moving ball?
As shown in figure, a 70 kg garden roller is pushed with a force of F = 200 N at an angle of 30° with horizontal. The normal reaction on the roller is: (Given: g = 10 ms−2)
