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Tec 114: Basic Mechanics Question Paper
Tec 114: Basic Mechanics
Course:Bachelor Of Technology In Chemical And Process Engineering
Institution: Moi University question papers
Exam Year:2012
MOI UNIVERSITY
UNIVERSITY EXAMINATIONS 2011/2012 ACADEMIC YEAR
FIRST YEAR FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF ENGINEERING
COURSE CODE: TEC 114
COURSE TITLE: BASIC MECHANICS
INSTRUCTIONS TO CANDIDATES
Kindly attempt all the questions.
Question One
a) A body of mass m on a rough inclined plane at 300 to the horizontal is steadily moved up the plane by a force of 200N applied upwards parallel to the plane. If the force is reduced to 70N, the body slides steadily downwards. Find the values of m and the coefficient of friction. [6 marks]
b) A load of 300g will just start to slide down a slope of 250:
i. What force will be required to haul up the load at a constant speed? [2.5 marks]
ii. Find the minimum force that will be required to haul up the load. [2 marks]
c) A ladder of negligible weight is propped up against a rough vertical wall. The coefficient of friction is the same for the wall and the ground. Top of the ladder is 12 metres above the ground and the bottom is 750cm from the base of the wall. If a woman climbs the ladder, find the minimum value of the coefficient of friction so that she reaches the top of the ladder before slip takes place. [3.5 marks]
Question Two
a) The ratio of the initial velocities of two similar spheres of equal masses is 2:3. If the velocity of the slow moving sphere is 10m/s just before an elastic collision takes place, find their final velocities. [4 marks]
b) A 2 ton car is to go over a turn whose radius is 750 meters and the angle of the slope is 50. The coefficient of friction between the road and the wheels is 0.5. What should be maximum speed of the car so that it may just go over the turn without slipping? [6 marks]
c) A weight is attached to a chord which is wound round a pulley whose diameter is 1.75 meters. The initial angular velocity of the pulley is 4 rad/s and the weight accelerates it at 0.3 rad/s2 for 10 seconds. Determine:
i. The final angular velocity and the displacement of the pulley. [2 marks]
ii. The linear acceleration, velocity and displacement of the tension weight at the end of 10 seconds. [2 marks]
Question Three
a) A body of mass 2250g hangs from a string of length 900mm. Calculate the stiffness of a spring required to give the same period as a pendulum when carrying the same mass. What is the frequency of oscillation? [6 marks]
b) The simple pendulum in part (a) above is hang inside a moving vehicle accelerating smoothly at 2.4m/s2. Calculate the horizontal displacement of the bob, if the bob is not set swinging.[3.5 marks]
c) In a simple crank and connecting rod mechanism, the crank is 50mm long and the connecting rod is 350mm long. The crank is 300 from the top dead center position.
i. Find the velocity and the acceleration of the piston at 10 rad/s. [4 marks]
ii. What is the maximum velocity and acceleration of the piston [1 mark]
Question four
a) Find the velocity and direction of a projection of a shot which passes in a horizontal direction just over the top of a wall which is 150 meters off and 76 meters high. [4 marks]
b) A body travelling along a horizontal path collides with a stationary body on its path. Upon collision both bodies coalesce and move on together in the direction of motion. Show that the energy lost after the impact is given by the expression:1/2m1u12[1-m1/m1+m2] where the symbols have their usual meaning. [3 marks]
c) A pile driving hammer of mass 0.5 ton falls 2.5meters from rest onto a pile of 145kg. There is no rebound and the pile is driven 150mm into the ground. Find the existing common velocity after the impact and the average force of the ground in bringing the pile and the hammer to rest. [7 marks]
Question Five
a) A screw jack carries a load of 4KN. It has a square thread single start screw of 20mm pitch and 50mm mean diameter. If the coefficient of friction between the nut and the screw is 0.22, calculate the torque to raise the load and the efficiency of the screw. What is the torque to lower the load? [3.5 marks]
b) A boy kicks a ball infront of a wall. The ball is git at an angle of 400 and just passes over the wall of about 3M. If the wall is about 67% of the maximum height the ball can reach, determine the velocity an direction just after the ball bounces from the ground if the coefficient of restitution between the ball and the ground is 0.8. `[10.5 marks]
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