Advertisements
Advertisements
Question
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?
Advertisements
Solution
Mass of the monkey, m = 15 kg,
Acceleration of the monkey in the upward direction, a = 1 m/s2
The free-body diagram of the monkey is shown below:
From the free-body diagram,
T − [15g + 15(a)] = 0
T − [15g + 15(1)] = 0
⇒ T = 5 (10 + 1)
⇒ T = 15 × 11 = 165 N
The monkey should apply a force of 165 N to the rope.
Initial velocity, u = 0
s = 5 m
Using, \[s = ut + \frac{1}{2}a t^2\], we get:
\[5 = 0 + \left( \frac{1}{2} \right) \times 1 \times t^2 \]
\[ \Rightarrow t^2 = 5 \times 2\]
\[ \Rightarrow t = \sqrt{10} s\]
Hence, the time required to reach the ceiling is \[\sqrt{10} s\]
APPEARS IN
RELATED QUESTIONS
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 monkey of mass 40 kg climbs on a rope in given Figure which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey
(a) climbs up with an acceleration of 6 m s–2
(b) climbs down with an acceleration of 4 m s–2
(c) climbs up with a uniform speed of 5 m s–1
(d) falls down the rope nearly freely under gravity?
(Ignore the mass of the rope).
When a horse pulls a cart, the force that helps the horse to move forward is the force exerted by
If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be
(a) going up with increasing speed
(b) going down with increasing speed
(c) going up with uniform speed
(d) going down with uniform speed
A person says that he measured the acceleration of a particle to be non-zero even though no force was acting on the particle.
A block of mass 0.2 kg is suspended from the ceiling by a light string. A second block of mass 0.3 kg is suspended from the first block by another string. Find the tensions in the two strings. Take g = 10 m/s2.
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.
Calculate the tension in the string shown in the following figure. The pulley and the string are light and all the surfaces are frictionless. Take g = 10 m/s2.
Find the acceleration of the blocks A and B in the three situations shown in the following figure.
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 tennis ball and a cricket ball , both are stationary. To start motion in them .
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 .
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.
Calculate the velocity of a body of mass 0.5 kg, when it has a linear momentum of 5 Ns.
Multiple Choice Question. Select the correct option.
The impulse of a body is equal to:
The INCORRECT statement about Newton's second law of motion is
A metre scale is moving with uniform velocity. This implies ______.
A cricket ball of mass 150 g has an initial velocity `u = (3hati + 4hatj)` m s−1 and a final velocity `v = - (3hati + 4hatj)` m s−1 after being hit. The change in momentum (final momentum-initial momentum) is (in kg m s1)
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?
