Advertisements
Advertisements
प्रश्न
A ball of mass 50 g moving at a speed of 2.0 m/s strikes a plane surface at an angle of incidence 45°. The ball is reflected by the plane at equal angle of reflection with the same speed. Calculate (a) the magnitude of the change in momentum of the ball (b) the change in the magnitude of the momentum of the ball.
Advertisements
उत्तर
It is given that:
Mass of the ball = 50 g =
\[0 . 05 \text{ Kg}\]
Speed of the ball, v = 2.0 m/s
Incident angle = 45˚
\[v = 2 \cos 45^\circ \hat i - 2 \sin 45^\circ \hat j \]
\[v' = - 2 \cos 45^\circ \hat i - 2 \sin 45^\circ \hat j\]
\[(a) \text{ Change in momentum } = m \vec{v} - m \vec{v} '\]
\[ = 0 . 05\left( 2 \cos 45^\circ\ \hat i - 2 \sin 45^\circ \hat j \right) - 0 . 05\left( - 2 \cos 45^\circ \hat i - 2 \sin 45^\circ \hat j \right)\]
\[ = 0 . 1 \cos 45^\circ\ \hat i - 0 . 1 \sin 45^\circ \ \hat j + 0 . 1 \cos 45^\circ \ \hat i + 0 . 1 \sin 45^\circ\ \hat j\]
\[ = 0 . 2 \cos 45^\circ\ \hat i \]
\[ \therefore \text{ Magnitude }= \frac{0 . 2}{\sqrt{2}} = 0 . 14 \text{ Kg m/s}\]
(b) The change in magnitude of the momentum of the ball,
\[\left| \vec{P}_2 \right| - \left| \vec{P}_1 \right| = 2 \times 0 . 5 - 2 \times 0 . 5 = 0\]
i.e. There is no change in magnitude of the momentum of the ball.
APPEARS IN
संबंधित प्रश्न
If the linear momentum of a particle is known, can you find its kinetic energy? If the kinetic energy of a particle is know can you find its linear momentum?
Suppose we define a quantity 'Linear momentum' as linear momentum = mass × speed.
The linear momentum of a system of particles is the sum of linear momenta of the individual particles. Can we state principle of conservation of linear momentum as "linear momentum of a system remains constant if no external force acts on it"?
Use the definition of linear momentum from the previous question. Can we state the principle of conservation of linear momentum for a single particle?
Consider the situation of the previous problem. Take "the table plus the ball" as the system. friction between the table and the ball is then an internal force. As the ball slows down, the momentum of the system decreases. Which external force is responsible for this change in the momentum?
Consider the following two statements:
(A) Linear momentum of a system of particles is zero.
(B) Kinetic energy of a system of particles is zero.
A nucleus moving with a velocity \[\vec{v}\] emits an α-particle. Let the velocities of the α-particle and the remaining nucleus be v1 and v2 and their masses be m1 and m2.
A shell is fired from a cannon with a velocity V at an angle θ with the horizontal direction. At the highest point in its path, it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. The speed of the other piece immediately after the explosion is
In an elastic collision
(a) the kinetic energy remains constant
(b) the linear momentum remains constant
(c) the final kinetic energy is equal to the initial kinetic energy
(d) the final linear momentum is equal to the initial linear momentum.
A man of mass 50 kg starts moving on the earth and acquires a speed 1.8 m/s. With what speed does the earth recoil? Mass of earth = 6 × 1024 kg.
A gun is mounted on a railroad car. The mass of the car, the gun, the shells and the operator is 50 m where m is the mass of one shell. If the velocity of the shell with respect to the gun (in its state before firing) is 200 m/s, what is the recoil speed of the car after the second shot? Neglect friction.
Consider a head-on collision between two particles of masses m1 and m2. The initial speeds of the particles are u1 and u2 in the same direction. the collision starts at t = 0 and the particles interact for a time interval ∆t. During the collision, the speed of the first particle varies as \[v(t) = u_1 + \frac{t}{∆ t}( v_1 - u_1 )\]
Find the speed of the second particle as a function of time during the collision.
In a gamma decay process, the internal energy of a nucleus of mass M decreases, a gamma photon of energy E and linear momentum E/c is emitted and the nucleus recoils. Find the decrease in internal energy.
A block of mass 2.0 kg is moving on a frictionless horizontal surface with a velocity of 1.0 m/s (In the following figure) towards another block of equal mass kept at rest. The spring constant of the spring fixed at one end is 100 N/m. Find the maximum compression of the spring.
A block of mass 200 g is suspended through a vertical spring. The spring is stretched by 1.0 cm when the block is in equilibrium. A particle of mass 120 g is dropped on the block from a height of 45 cm. The particle sticks to the block after the impact. Find the maximum extension of the spring. Take g = 10 m/s2.
A bullet of mass 10 g moving horizontally at a speed of 50√7 m/s strikes a block of mass 490 g kept on a frictionless track as shown in figure. The bullet remains inside the block and the system proceeds towards the semicircular track of radius 0.2 m. Where will the block strike the horizontal part after leaving the semicircular track?
The blocks shown in figure have equal masses. The surface of A is smooth but that of Bhas a friction coefficient of 0.10 with the floor. Block A is moving at a speed of 10 m/s towards B which is kept at rest. Find the distance travelled by B if (a) the collision is perfectly elastic and (b) the collision is perfectly inelastic.
A solid sphere of mass m is released from rest from the rim of a hemispherical cup so that it rolls along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup.
The following figure shows a small spherical ball of mass m rolling down the loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a radius R.
(a) Find the kinetic energy of the ball when it is at a point A where the radius makes an angle θ with the horizontal.
(b) Find the radial and the tangential accelerations of the centre when the ball is at A.
(c) Find the normal force and the frictional force acting on the if ball if H = 60 cm, R = 10 cm, θ = 0 and m = 70 g.
