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
From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s−1. Calculate the initial recoil velocity of the rifle.
An object of mass 1 kg travelling in a straight line with a velocity of 10 ms−1 collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.
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?
state whether momentum is scalar or vector.
Explain why, it is easier to stop a tennis ball than a cricket ball moving with the same speed.
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 ?
A plastic ball and a clay ball of equal masses, travelling in the same direction with equal speeds, strike against a vertical wall. From which ball does the wall receive a greater amount of momentum ?
Name the principle on which a rocket works.
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
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 ?
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 girl of mass 50 kg jumps out of a rowing boat of mass 300 kg on to the bank, with a horizontal velocity of 3 m/s. With what velocity does the boat begin to move backwards ?
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 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 vessel at rest explodes into three pieces. Two pieces having equal masses fly-off perpendicular to one another with the same velocity 30 meter per second. The third piece has three times mass of each of other piece. The magnitude and direction of the velocity of the third piece will be
Two billiard balls A and B, each of mass 50 g and moving in opposite directions with speed of 5 ms–1 each, collide and rebound with the same speed. If the collision lasts for 10–3 s, which of the following statements are true?
- The impulse imparted to each ball is 0.25 kg ms–1 and the force on each ball is 250 N.
- The impulse imparted to each ball is 0.25 kg ms–1 and the force exerted on each ball is 25 × 10–5 N.
- The impulse imparted to each ball is 0.5 Ns.
- The impulse and the force on each ball are equal in magnitude and opposite in direction.
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 ______.
