Advertisements
Advertisements
Question
Two balls, A (mass 3kg) and B (mass 4kg), are moving with velocities 25 m/s and 40 m/s respectively (Refer Figure 15). Before impact, the direction of velocity of two balls are 300 and 500 with the line joining their centers as shown in Figure 15. If coefficient of restitution for the impact is 0.78, find the magnitude and the direction of velocities of the balls after the impact.
Solution
uAx = 25sin(30) = 12.5 m/s
uAy = 25cos(30) = 21.65 m/s
uBx = 40sin(50) = 30.64 m/s
uBy = -40cos(50) = -25.71 m/s
Momentum is conserved only along the line of action.
mAuAy + mBuBy = mAvAy + mBuBy
3(21.65) + 4(-25.71) = 3vAy + 4vBy
3vAy + 4vBy = -37.89 …..(1)
`e = (VBy-V)/(UAy-UBy)`
`0.78 = (VBy - VAy)/(21.65+25.71`
vBy – vAy = 36.9408 …..(2)
Solving (1) and (2)
vAy = -26.52 m/s = 26.52 m/s↓
vBy = 10.42 m/s↑
The magnitude of the velocities and direction of A and B are 26.52 m/s downwards and 10.42 m/s upwards respectively.
APPEARS IN
RELATED QUESTIONS
Find the co-ordinate of the centroid of the area as shown in the given figure.
The position vector of a particle which moves in the X-Y plane is given by 𝒓̅ = (3t3-4t2)𝒊̅ + (0.5t4)𝒋̅
Two balls having 20kg and 30 kg masses are moving towards each other with velocities of 10 m/s and 5 m/s respectively as shown in the figure.
If after the impact ,the ball having 30 kg mass is moving with 6 m/s velocity to the right then determine the coefficient of restitution between the two balls.
The V-X graph of a rectilinear moving particle is shown. Find the acceleration of the particle at 20m,80 m and 200 m
A bar 2 m long slides down the plane as shown.The end A slides on the horizontal floor with a velocity of 3 m/s.Determine the angular velocity of rod AB and the velocity of end B for the position shown.
A 500 N Crate kept on the top of a 15° sloping surface is pushed down the plane with an initial velocity of 20m/s. If μs = 0.5 and μk = 0.4, determine the distance travelled by the block and the time it will take as it comes to rest.
Given: Weight of crate = 500 N
Initial velocity(u) = 20 m/s
μs = 0.5
μk = 0.4
θ = 15°
Final velocity (v) = 0 m/s
To find: Distance travelled by the block Time it will take before coming to rest
Derive the equation of path of a projectile and hence show that equation of path of projectile is a parabolic curve.
particle is moving in X-Y plane and it’s position is defined by`bar r=(3/2 t^2)bar l+(2/3 t^3) barJ "Find radius of curvature when t=2sec." `
A Force of 100 N acts at a point P(-2,3,5)m has its line of action passing through Q(10,3,4)m. Calculate moment of this force about origin (0,0,0).
Blocks P1 and P2 are connected by inextensible string.Find velocity of block P1,if it falls by 0.6 m starting from rest.
The co-efficient of friction is 0.2.The pulley is frictionless.
Co-ordinate distance are in m units for the space frame in figure.
There are 3 members AB,AC and AD.There is a force W=10 kN acting at A in a vertically upward direction.
Determine the tension in AB,AC and AD.
A glass ball is dropped on a smooth horizontal floor from which it bounces to a height of 9m.On the second bounce it rises to a height of 6 m.From what height was the ball dropped and find the coefficient of restitution between the glass and the floor.
Given : First bounce height = 9 m
Second bounce height = 6 m
To find : Co-efficient of restitution
Angular velocity of connector BC is 4 r/s in clockwise direction.What is the angular velocities of cranks AB and CD?
The acceleration time diagram for a linear motion is shown. Construct velocity time diagram and displacement time diagram for the motion assuming that the motion starts with a initial velocity of 5 m/s from the starting point.
Given : Acceleration time graph
To draw : Velocity time graph
Displacement time graph
A circle of diameter 1.5 m is cut from a composite plate.Determine the centroid of the remaining area of plate.
A rod AB has an angular velocity of 2 rad/sec,counter clock wise as shown.End C of rod BC is free to move on a horizontal surface.Determine:
(1)Angular velocity of rod BC
(2)Velocity of C
Given : ωAB=2 rad/sec (anti clockwise)
To find : ωBC
VC
Velocity-time diagram for a particle travelling along a straight line is shown in Figure 10. Draw acceleration-time and displacement-time diagram for the particle. Also find important values of acceleration and displacement.
A 75kg person stands on a weighing scale in an elevator. 3 seconds after the motion starts from rest, the tension in the hoisting cable was found to be 8300N. Find the reading of the scale, in kg during this interval. Also find the velocity of the elevator at the end of this interval. The total mass of the elevator, including mass of the person and the weighing scale, is 750kg. If the elevator is now moving in the opposite direction, with same magnitude of acceleration, what will be the new reading of the scale?
Two springs, each having stiffness of 0.6N/cm and length 20 cm are connected to a ball B of weight 50N. The initial tension developed in each spring is 1.6N. The arrangement is initially horizontal, as shown in Figure 14. If the ball is allowed to fall from rest, what will be its velocity at D, after it has fallen through a height of 15 cm?
