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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.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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?
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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?
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
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.
Concept: Velocity and Acceleration in Terms of Rectangular Co-ordinate System
A particle moves in x-y plane with acceleration components ax = -3m/s2 and ay = -16t m/s2. If its initial velocity is V0 = 50m/s directed at 350 to the x–axis, compute the radius of curvature of the path at t = 2 sec.
Concept: Tangentialand Normal Component of Acceleration
Find an expression for maximum range of a particle which is projected with an initial velocity of ‘u’ inclined at an angle of ‘β’ with the horizontal.
Concept: Motion Curves (a-t, v-t, s-t curves)
Compute the resultant of three forces acting on the plate shown in the figure. Locate it’s intersection with AB and BC.
Concept: Velocity Diagrams for Bodies in Plane Motion.
Rod AB of length 3 m is kept on a smooth plane as shown in the given figure.The velocity of end A is 5 m/s along the inclined plane.Locate the ICR and find velocity of end B.
Given : Length of rod AB = 3m
va = 5 m/s
To find: ICR
Velocity of end B
Concept: Instantaneous Center of Rotation for the Velocity
Using Instantaneous Centre of Rotation (ICR) method, find the velocity of point A for the instant shown in Figure 2. Collar B moves along the vertical rod, whereas link AB moves along the plane which is inclined at 250. Ɵ = 450
Concept: Instantaneous Center of Rotation for the Velocity
From the top of a tower, 28 m high, a stone is thrown vertically up with a velocity of 9m/s. After how much time will the stone reach the ground? With what velocity does it strike the ground?
Concept: Velocity Diagrams for Bodies in Plane Motion.
The link CD of the mechanism shown in Figure 7 is rotating in counterclockwise direction at an angular velocity of 5 rad/s. For the given instance, determine the angular velocity of link AB.
Concept: Instantaneous Center of Rotation for the Velocity
A particle starts from rest from origin and it’s acceleration is given by a = `k/(x+4)^2 m⁄s^2`.Knowing that v = 4 m/s when x = 8m,find :
(1)Value of k
(2)Position when v = 4.5 m/s
Given : Particle starts from rest
a = `k/(x+4)^2 m⁄s^2`
v = 4m/s at x = 8m
To find : Value of k and position when v= 4.5m/s
Concept: Introduction to Basic Concepts
A 50 N collar slides without friction along a smooth and which is kept inclined at 60o to the horizontal.
The spring attached to the collar and the support C.The spring is unstretched when the roller is at A(AC is horizontal).
Determine the value of spring constant k given that the collar has a velocity of 2.5 m/s when it has moved 0.5 m along the rod as shown in the figure.
Concept: Principle of Work and Energy
b)A cylinder has a mass of 20kg and is released from rest when h=0 as shown in the figure.Determine its speed when h=3m.The springs have an unstretched length of 2 m.Take k=40 N/m.
Given : m=20 kg
h=0
k=40 N/m
To find : Speed when h=3m
Concept: Principle of Work and Energy
Just before they collide,two disk on a horizontal surface have velocities shown In figure.
Knowing that 90 N disk A rebounds to the left with a velocity of 1.8 m/s.Determine the rebound velocity of the 135 N disk B.Assume the impact is perfectly elastic.
Concept: Law of Conservation of Momentum
What are the main causes of soil degradation?
Concept: Introduction to Depletion of Natural Resources
How increasing population is exerting extra pressure on land and mineral resource discuss.
Concept: Global Crisis Related to – Population, Water, Sanitation and Land
What do you mean by land filling? Explain briefly.
Concept: Global Crisis Related to – Population, Water, Sanitation and Land
Explain case study of kedarnath.
Concept: Definition, Scope and Importance of Environmental Study
Explain depleting nature of forests: causes, effects and prevention.
Concept: Introduction to Depletion of Natural Resources
