Advertisements
Advertisements
प्रश्न
A stream of water flowing horizontally with a speed of 15 m s–1 gushes out of a tube of cross-sectional area 10–2 m2, and hits a vertical wall nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound?
Advertisements
उत्तर १
Speed of the water stream, v = 15 m/s
Cross-sectional area of the tube, A = 10–2 m2
Volume of water coming out from the pipe per second,
V = Av = 15 × 10–2 m3/s
Density of water, ρ = 103 kg/m3
Mass of water flowing out through the pipe per second = ρ × V = 150 kg/s
The water strikes the wall and does not rebound. Therefore, the force exerted by the water on the wall is given by Newton’s second law of motion as:
F = Rate of change of momentum = `(triangleP)/(trianglet)`
`= "mv"/t`
= 150 x 15 = 2250 N
उत्तर २
In one second, the distance travelled is equal to the velocity v.
Volume of water hitting the wall per second, V = av where a is the cross-sectional area of the tube and v is the speed of water coming out of the tube.
V = 10-2 m2 x 15 ms-1 = 15 x 10-2 m3 s-1
Mass of water hitting the wall per second = 15 x 10-2 x 103 kg s-1 = 150 kg s-1 [v density of water = 1000 kg m-3] Initial momentum of water hitting the wall per second
= 150 kg s-1 x 15 ms-1 = 2250 kg ms-2 or 2250 N Final momentum per second = 0
Force exerted by the wall = 0 – 2250 N = – 2250 N Force exerted on the wall = – (- 2250) N = 2250 N.
संबंधित प्रश्न
Two objects, each of mass 1.5 kg are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 m s−1 before the collision during which they stick together. What will be the velocity of the combined object after collision?
A shell of mass 0.020 kg is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m s–1, what is the recoil speed of the gun?
Name the physical quantity which is considered to be a measure of the quantity of motion of a body.
What is the total momentum of the bullet and the gun before firing ?
Name the physical quantity whose unit is kg.m/s.
Explain why, it is easier to stop a tennis ball than a cricket ball moving with the same speed.
Explain how, a karate player can break a pile of tiles with a single blow of his hand.
What is the momentum in kg.m/s of a 10 kg car travelling at (a) 5 m/s (b) 20 cm/s, and (c) 36 km/h ?
Define momentum of a body. On what factors does the momentum of a body depend ?
Calculate the change in momentum of a body weighing 5 kg when its velocity decreases from 20 m/s to 0.20 m/s.
Which physical principle is involved in the working of a jet aeroplane ?
Fill in the following blanks with suitable words :
In collisions and explosions, the total _____________ remains constant, provided that no external _____________ acts.
A 10 g bullet travelling at 200 m/s strikes and remains embedded in a 2 kg target which is originally at rest but free to move. At what speed does the target move off ?
An unloaded truck weighing 2000 kg has a maximum acceleration of 0.5 m/s2. What is the maximum acceleration when it is carrying a load of 2000 kg ?
Why would an aircraft be unable to fly on the moon ?
A truck of mass 500 kg moving at 4 m/s collides with another truck of mass 1500 kg moving in the same direction at 2 m/s. What is their common velocity just after the collision if they move off together ?
A man wearing a bullet-proof vest stands still on roller skates. The total mass is 80 kg. A bullet of mass 20 grams is fired at 400 m/s. It is stopped by the vest and falls to the ground. What is then the velocity of the man?
Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of the initial and final momentums of the ball are the same. Yet, it is not an example of conservation of momentum. Explain why?
A girl riding a bicycle along a straight road with a speed of 5 ms–1 throws a stone of mass 0.5 kg which has a speed of 15 ms–1 with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown? What is the change in speed, if so?
A monkey of mass 20 kg rides on a 40 kg trolley moving with constant speed of 8 m/s along a horizontal track If the monkey jumps vertically to grab the overhanging branch of a tree, the speed of the trolley after the monkey has jumped off is ______.
