Advertisements
Advertisements
Question
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.)
Advertisements
Solution
- For t < 0
For t<0, the graph of position versus time is denoted as BO, which indicates that the displacement of the particle is zero, i.e., the particle is stationary at the origin. Consequently, the force exerted on the particle must be zero. - For t > 4 s
For t>4 s, the position-time graph segment AC runs parallel to the time axis, indicating that the particle maintains a position 3 metres from the origin, implying it is stationary. Therefore, the force acting on the particle is zero. - For 0 < t < 4
Between 0 < t < 4 s, the position-time graph labelled OA displays a constant slope, which indicates that the velocity of the particle remains constant during this interval, meaning the particle has zero acceleration. Consequently, the force on the particle must be zero.
- For t < 0
- At t = 0
Impulse = Change in momentum
= mv – mu
Mass of the particle, m = 4 kg
Initial velocity of the particle, u = 0
Final velocity of the particle, `v = 3/4 "m/s"`
∴Impulse = `4(3/4 - 0) = 3 kg "m/s"`
At t = 4 s
Initial velocity of the particle, `u = 3/4 "m/s"`
Final velocity of the particle, v = 0
∴ Impulse = `4(0-3/4)` = -3 kg m/s
APPEARS IN
RELATED QUESTIONS
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.
A block of mass 15 kg is placed on a long trolley. The coefficient of static friction between the block and the trolley is 0.18. The trolley accelerates from rest with 0.5 ms–2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground, (b) an observer moving with the trolley.
A car accelerates on a horizontal road due to the force exerted by.
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 particle of mass 0.3 kg is subjected to a force F = −kx with k = 15 N/m. What will be its initial acceleration if it is released from a point x = 20 cm?
A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the following figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up. Find the force when the man is at a depth h.
In the following figure shows a uniform rod of length 30 cm and mass 3.0 kg. The strings shown in the figure are pulled by constant forces of 20 N and 32 N. Find the force exerted by the 20 cm part of the rod on the 10 cm part. All the surfaces are smooth and the strings and the pulleys are light.
In the following figure, m1 = 5 kg, m2 = 2 kg and F = 1 N. Find the acceleration of either block. Describe the motion of m1 if the string breaks but F continues to act.
Find the mass M of the hanging block in the following figure that will prevent the smaller block from slipping over the triangular block. All the surfaces are frictionless and the strings and the pulleys are light.
Define linear momentum and state its S.I. unit.
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 : The velocity acquired by the body
A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate: The velocity acquired by the body.
A body of mass 200 g is moving with a velocity of 5 ms−1. If the velocity of the body changes to 17 ms−1, calculate the change in linear momentum of the body.
Use Newton's second law to explain the following:
While catching a fast moving ball, we always pull our hands backwards.
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 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?
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.
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)
