Advertisements
Advertisements
प्रश्न
Figure shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s–2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)
Advertisements
उत्तर १
Mass of the man, m = 65 kg
Acceleration of the belt, a = 1 m/s2
Coefficient of static friction, μ = 0.2
The net force F, acting on the man is given by Newton’s second law of motion as:
`F_"net"` = ma = 65 × 1 = 65 N
The man will continue to be stationary with respect to the conveyor belt until the net force on the man is less than or equal to the frictional force fs, exerted by the belt, i.e.,
`F_"net"^' = f_s`
`ma^' = mu mg`
∴a' = 0.2 × 10 = 2 m/s2
Therefore, the maximum acceleration of the belt up to which the man can stand stationary is 2 m/s2.
उत्तर २
Here acceleration of conveyor belt a = 1 ms-2, μs= 0.2 and mass of man m = 65 kg. t As the man is in an accelerating frame, he experiences a pseudo force Fs= ma as shown in figure
Hence to maintain his equilibrium, he exerts a force F = – Fs = ma = 65 x 1 = 65 N in forward direction i.e., direction of motion of belt.
∴Net force acting on man = 65 N (forward)
As shown in fig. (b), the man can continue to be stationary with respect to belt, if force of friction
`mu_s N = mu_s mg = ma_"max"`
`a_"max" = mu_s g = 0.2 xx 10 = 2 m s^(-2)`
संबंधित प्रश्न
A hockey ball of mass 200 g travelling at 10 m s−1 is struck by a hockey stick so as to return it along its original path with a velocity at 5 m s−1. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
Two billiard balls, each of mass 0.05 kg, moving in opposite directions with speed 6 ms-1collide and rebound with the same speed. What is the impulse imparted to each ball due to the other?
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?
What is the total momentum of the bullet and the gun before firing ?
Explain how, a karate player can break a pile of tiles with a single blow of his hand.
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.
A man throws a ball weighing 500 g vertically upwards with a speed of 10 m/s.
- What will be its initial momentum ?
- What would be its momentum at the highest point of its flight ?
State the relation between the momentum of a body and the force acting on it.
A gun of mass 3 kg fires a bullet of mass 30 g. The bullet takes 0.003 s to move through the barrel of the gun and acquires a velocity of 100 m/s. Calculate:
- the velocity with which the gin recoils.
- the force exerted on gunman due to recoil of the gun
Explain why, a cricket player moves his hands backwards while catching a fast cricket ball.
State the law of conservation of momentum.
Why would an aircraft be unable to fly on the moon ?
Explain why it is possible for a small animal to fall from a considerable height without any injury being caused when it reaches the ground.
A boy of mass 50 kg running at 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s. What is their common velocity ?
A ball X of mass 1 kg travelling at 2 m/s has a head-on collision with an identical ball Y at rest. X stops and Y moves off. Calculate the velocity of Y after the collision.
A heavy car A of mass 2000 kg travelling at 10 m/s has a head-on collision with a sports car B of mass 500 kg. If both cars stop dead on colliding, what was the velocity of car B ?
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?
A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500 m. It falls on the ground at a distance of 400 m from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 ms–2)
