Advertisements
Advertisements
Question
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
Solution
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
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.
Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to
- A,
- B along the direction of string. What is the tension in the string in each case?
Two masses 8 kg and 12 kg are connected at the two ends of a light, inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
You are travelling in a car. The driver suddenly applies the brakes and you are pushed forward. Why does this happen?
A force \[\vec{F} = \vec{v} \times \vec{A}\] is exerted on a particle in addition to the force of gravity, where \[\vec{v}\] is the velocity of the particle and \[\vec{A}\] is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?
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.
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.
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.
A tennis ball and a cricket ball , both are stationary. To start motion in them .
Write the mathematical form of Newton's second law of motion. State the conditions if any.
Use Newton's second law of motion to explain the following instance :
An athlete prefers to land on sand instead of hard floor while taking a high jump .
A car is moving with a uniform velocity 30 ms-1. It is stopped in 2 s by applying a force of 1500 N through its brakes. Calculate the following values : The change in momentum of car.
How long will a stone take to fall to the ground from the top of a building 80 m high
Calculate the velocity of a body of mass 0.5 kg, when it has a linear momentum of 5 Ns.
Name the physical entity used for quantifying the motion of a body.
Use Newton's second law to explain the following:
We always prefer to land on sand instead of hard floor while taking a high jump.
What do you mean by the conservation of momentum? Briefly, explain the collision between two bodies and the conservation of momentum.
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)
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
A woman throws an object of mass 500 g with a speed of 25 ms1.
- What is the impulse imparted to the object?
- If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object?
