Kinematics of Particles Worksheet - 1

1.   The acceleration of a particle performing rectilinear motion is given by a = k.t m/s². It is found that v = -24 m/s  when t = 0 and v = 48 m/s when t = 4 sec. Also x = 0 at     t = 3 sec. Find the value of ‘k’ and also the position, velocity and acceleration of the particle at t = 2 sec.

2.   The acceleration of a particle performing rectilinear motion is given by a= -0.05 v² m/s² Knowing that v = 20 m/s at x = 0 find,

a) The position of the particle at v = 15 m/s  

b) The particle’s accelerations at x = 50 m.

3.   The motion of a particle moving in straight line is given by the expression                    s = t³ – 3t² + 2t + 5 where ‘s’ is the displacement in meters and ‘t’ is time in seconds. Determine

a)   Velocity and acceleration after 4 sec.

b)   Maximum or minimum velocity and corresponding displacement and

c)   time at which velocity is zero.

4.   The position of a particle moving along a straight line is defined by the relation            x = t³ – 9t² + 15t + 18 where x is expressed in meters and t in seconds. Determine the time, position and acceleration of the particle when its velocity becomes zero.

5.   Acceleration of a particle is given by a = -kx^-3  m/s² . Knowing at x = 2 m, v = 0 and at x = 0.5 m, v = 3 m/s. Determine

a)   The value of ‘k’

b)   The particle’s velocity at x = 1m.

6.   The velocity relation of a rectilinear moving particle is defined as v = 4t² - 3t – 1 m/s. At t = 0, x = -4 m. Determine

a.    the time at which the particle reverses its sense of motion

At t = 3 sec.

a)   Acceleration

b)   position

c)   Displacement

d)   Distance travelled.

7.   A particle performing rectilinear motion has its acceleration given by a = (2 – 5 t) m/s².  At t = 4 sec its velocity is 15 m/s and t = 8 sec. its position is 60 m. Find at       t = 0, the particles position, velocity and acceleration. Also find the time when its velocity becomes zero.

8.   The acceleration of a vehicle at any instant is given by the expression a = ( ) m/s² If the vehicles starts from rest, find its velocity when its displacement is 125 m. Also find its displacement when its velocity is 10 m/s.

****************************************************************************************

 Get All Engineering Mechanics Lectures By Mechcrack.

Enroll this course  : https://imojo.in/2rfQex

Centroid Worksheet - 1

1.   Find the centroid of the shaded area shown.

2. Determine the centroid of the shaded plane area shown.

3.   Locate centroid of the shaded area shown in figure.

Friction Worksheet - 2

1.Two blocks A and B of weight 500 N and 750 N respectively are connected by a cord that passes over a frictionless pulley as shown in figure. µ between the block A and inclined plane is 0.4 and the between the block B and the inclined plane is 0.3. Determine the force P to be applied to block B to produce the impending motion of block B down the plane.

2. Determine the maximum value of P that can be applied to the roller shown in figure without causing it to rotate. Coefficient of friction for all contact surfaces is 0.5.

3.   Two 6^o wedges are used to push the block horizontally as shown. Calculate the minimum force P required to push the block of weight 10000 N. µ = 0.25 for all surfaces.

4.   A block weighing 1000 N is raised against a surface inclined at 60^o to the horizontal by means of a 15^o wedge as shown in figure. Find the horizontal force P which will just start the block to move if the coefficient of friction between all the surfaces of contact be 0.2. Assume the wedge to be of negligible weight.

Friction Worksheet - 1

1.   Explain coefficient of friction.

2.   List the laws of dry friction.

3.   Define Angle of friction and Angle of Repose.

4.   What is cone of friction?

5.   Differentiate between static and kinetic friction.

6.   “Friction is friend of man” comment on this statement.

7.   For the following cases find forces P needed to just impend the motion of the block. Take weight of block to be 100 N and coefficient of static friction at the contact surface to be 0.4.

8.Block A of weight 2000 N is kept on a plane inclined at 350. It is connected to weight B by an in-extensible string passing over a smooth pulley. Determine weight of B so that B just moves down. Take µ = 0.2

9.   Three blocks are placed on the surface one above the other as shown in figure. The static coefficient of friction between the surfaces is shown. Determine the maximum value of that can be applied before any slipping takes place.

Equilibrium of System Worksheet - 2

1.Find the reactions at A, B, C, and D. Neglect friction.

2.A roller of weight W=1000N rest on a smooth incline plane. It is kept from rolling down the plane by a string AC. Find the tension in the string and reaction at the point of contact D.

3.A uniform wheel of 800 mm diameter, weighing 6kN rests against a rigid rectangular block of 150 mm height as shown in figure. Find the least pull through the centre of the wheel required just to turn the wheel over the corner A of the block. Also find the reaction on the block .Take all the surface to be smooth.

Equilibrium of System Worksheet - 1

    1. The beam AB is loaded by forces and couples as shown. Find the reaction force offered by the supports to keep the system in equilibrium.

  2. A Man of 800N weight stands on a 10 m long uniform beam ABCD of self weight 2000N.The beam is supported by hinge at B and a rope whose one end is attached at C and the other end carries a counterweight W_B. Find the value of W_B needed to keep the beam in a Horizontal position as shown and also find the hinge reactions.

3. A heavy rod AB of length 3 m lies on horizontal ground .To lift the end B off the ground needs a vertical force of 200N. To lift A end off the ground needs a force 160 N. Find the weight of the rod and the position of centre of mass.

        4. Find analytically the support reaction at B and load P for the beam shown in figure if reaction at support A is zero.

5. Determine the intensity of distributed load w at the end C of the beam ABC for which the reaction at C is zero. Also calculate the reaction at B.

Worksheet-1 (Coplanar Forces)

1.   Define

a)   Force

b)   Moment of force

c)   Resultant

2.   State and prove Varignon’s theorem of moment.

3.   State the difference between Composition and Resolution of Forces.

4.  













Determine the resultant of the system of forces shown in figure. Locate the point where the resultant cuts the base AB.

5.   dam is subjected to three forces, 50kN on the upstream face AB, 30 kN force on the downstream inclined face and its own weight of 120kN as shown. Determine the single force and locate its point of intersection with the base AD assuming all the forces to lie in a single plane.