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Find the co-ordinate of the centroid of the area as shown in the given figure.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
The position vector of a particle which moves in the X-Y plane is given by 𝒓̅ = (3t3-4t2)𝒊̅ + (0.5t4)𝒋̅
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
The V-X graph of a rectilinear moving particle is shown. Find the acceleration of the particle at 20m,80 m and 200 m
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Derive the equation of path of a projectile and hence show that equation of path of projectile is a parabolic curve.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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." `
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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).
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
From (v-t) diagram find (1) Distance travelled in 10 second.
(2) Total distance travelled in 50 second.
(3) Retardation
Concept: Motion Curves (a-t, v-t, s-t curves)
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.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Angular velocity of connector BC is 4 r/s in clockwise direction.What is the angular velocities of cranks AB and CD?
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
Determine the speed at which the basket ball at A must be thrown at an angle 30o so that if makes it to the basket at B.
Also find at what speed it passes through the hoop.
Concept: Motion Curves (a-t, v-t, s-t curves)
Figure shows a collar B which moves upwards with constant velocity of 1.5 m/s.At the instant when θ=50o.Determine :
(i)The angular velocity of rod pinned at B and freely resting at A against 25o sloping ground.
(ii)The velocity of end A of the rod.
Concept: Motion Curves (a-t, v-t, s-t curves)
A circle of diameter 1.5 m is cut from a composite plate.Determine the centroid of the remaining area of plate.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
A particle falling under gravity travels 25 m in a particular second. Find the distance travelled by it in the next 3 seconds.
Given : Particle falls 25 m in a particular second
Sn=-25 m
u=0 m/s
To find : Distance travelled by it in next 3 seconds
Concept: Tangentialand Normal Component of Acceleration
