# Canadian Second Class ME  Applied Mechanics

### Test Question Examples: #1

The diameters of a barrel are 395 mm at each end, 477 mm at quarter and three quarter lengths. and 500 mm at midlength and the total length is 58l mm Using Simpson's first Rule, calculate the capacity of the barrel in liters.

The Shank of a Plain Steel Bolt is 20 mm Dia, it has a round head 35 mm Dia, end 20 mm thick and the overall length is 120 mm. A brass ring, 30 mm Dia, end 10 mm thick is forced onto the shank leaving a clearance of 70 mm between the head and ring Taking the densities of steel and brass as 7.86 and 8.4g/cm3 respectively, calculate the position of the center of gravity from the end of the shank.

A connecting rod is 2100 mm long between its top and bottom center its weight is 9.24 KN, and its center of gravity is at 1170 mm from the top end. If it hangs freely from the top, find the least force required at the bottom end to pull it 700 mm out of the vertical. Find also the force required of it is applied in a horizontal direction.

The speed of a generator is increased from 1000 to 1400 rpm in 8 seconds. Find the angular acceleration (rad/s2) and the number of revs turned during this time.

A triangular roof frame consists of a horizontal tie rod and two rafters inclined at 300 and 600 respectively to horizontal and is supported at the ends of its span as illustrated. If it carries a load of 4 kn at the tie apex, determine the resulting thrusts in the rafters, the tension in the tie rod and tic reactions of the supports.

If a force of 670 N is sufficient to draw a mass of one ton along a level surface; calculate the force required to draw a mass of one ton up an incline of 1 in 45.

A thin flywheel rim l.2 M dia. is made of cast iron of a density 7.21g/cm3. Find the sped in revs/min at which the stress due to centrifugal force will be 15MN/m2.

The effort wheel of a worm and worm chain block is 200 mm. Dia, the worm is single start and there are 40 teeth in the worm wheel. The load wheel is 125 mm dia. and the load carried by a snatch block on the loop of the lifting chain from the load wheel to the frame work of the machine. If the effort required to lift a load of 6.72 Kn is 160 N. Find the efficiency when lifting this load and the V. R. of this unit.

A crowbar 2 m long is used to move and object at one end of the bar. If the force required to move the object is 500 N and the maximum effort that could be exerted at the other end of the lever is 120 N. Calculate the max distance of the fulcrum from the end of the bar at which the load is located.

### Test Question Examples #2

A copper pipe is 76 mm inside dia. 6.35 mm thick and 3 mm long. The mass of the pipe is 43 kg. Calculate the relative density of the pipe.

A cylinder, a sphere and the base of a cone all have the same diameter. The heights of the cylinder and cone are each equal to the diameter of the sphere. Find the ratio of the volume of the cylinder and sphere relative to the volume of the cone.

A ballast tank 1.6 deep can be flooded by opening the sea suction valve for 2 hrs. l2 min it can be emptied with a ballast pump in 4 hrs. 24 min. Assume the tank as being empty and the pump started and seavalve opened simultaneously, calculate the depth of water in the tank after 1 hr. 36 min.

An inclined plane has an inclination of 1 in 8 and the coefficient of friction is 0.2 Calculate the force required to move a mass of 50 kg up the plane and the work done in moving the body through 3 m measured along the plane.

A screw jack is used to lift a mass of 500 kg. The lead of the screw is 12 mm. Calculate force required at the end of a 300 mm arm, efficiency is 28% Also determine velocity ratio the mechanical advantage.

A ships propellers are stopped when she Is traveling at 25 knots and the ship travels 4 km from then until she comes to rest, Find the time taken to rest in minutes and the average retardation in m/s2. One knot = 1 .852 km/h.

A cylindrical vessel made from 6.5 mm plate is 575 mm O.D. It is joined by "V" welding. The thickness of the weld being the same as the plate. The working pressure of this is 100kn/m2 The tensile strength of the plate is 41. 7MPa (MN/rn2 ), and the weld 386 MPa (MN/in2) Find the intensity of stress on the weld and on the factor of safety.

A derrick is 6m long. It is suspended from a vertical post by a topping lift 3m long at right angles to the vertical post. The mass of the derrick is 340Kg. and Its center of gravity Is at midlength. Find the tension in the topping lift and the force in the derrick.

A system of pulleys consists of an upper block fitted with 3 pulleys and a lower block fitted with 2 pulleys. An effort of 240 N is required to raise a body having a mass of 85 kg. Sketch the arrangement and calculate.
a) velocity ratio
c) efficiency
d) work done in lifting the body 50 m
a) the corresponding work done by the effort

### Test Question Examples #3

The mass of a propeller is 5 T and its center of gravity is 4 mm from center of rotation. Calculate the out of balance force when the propeller rotates at 110 RPM.

A uniform derrick is 10.7m long and has a mass of 430 kg. It is hinged at its lower end to a vertical post and slung at its upper end from the post by topping lift 4rn long. The topping lift makes an angle of l 20E to derrick. Find the magintude and nature of the forces in the topping lift and derrick due to the mass of the derrick.

How does the strength of a beam vary with respect to its length Width and depth? A beam is 30 mm wide 64 mm deep and l.3 m long. It can safely carry a load of 2.5 KN. Another beam loaded and supported in the same manner is 76 mm wide 165 mm deep and 2 m long. If the second beam is made of the same material as the first. Calculate the load it can carry safely.

A ball is thrown vertically upwards at a velocity of 20 m/s. Calculate (a) the time taken to reach the maximum height and (b) the maximum height obtained. Assume c/g = 9.8 l m/s2 and the air resistance to be negligible.

Two ships leave at the same time from the same port, one travels south east at 22 knots and the other due east at l 4 knots. Find the apparent speed and direction of the fast ship to the slow ship and the distance apart after 5 hours.

A tie bar made of mild steel of tensile strength 480 MPa is to carry a tensile load of 11.12 KN. Find its diameter allowing a factor of safety of 12.

The mass of a flywheel is 109 kg and its radius of gyration is 300 mm. Calculate the kinetic energy stored in it when rotating at 100, 200 and 300 RPM.

A fuel tank is 6m long, 7m wide and 4.8m deep. The fuel has a relative density of 0.8. Calculate the mass of fuel in the tank. If the engine consumes 14t per day, how many hours will it operate if the vessel Is to arrive in port with 15t in reserve.

The steam space of a boiler at the water level is 4.42m broad. The distance from the water level to the top of the boiler is l. 50m. The vertical height from the water level to the boiler shell at the quarter breadth is l .22m. Find the area of the end plate which is in the steam space.

### Test Question Examples #4

A beam 20 meter long, rests on two end supports and carries loads of 2, l .2 and l .6 KN at 8, l l and 15 meters respectively from left end. Find the magnitude of the reactions, neglecting weight of beam.

The speed and direction of a motor launch is changed from 9 knots due north to l l knots due west 30 seconds. Find the average acceleration in m/s2 .One knot = l .852 Kms.

On a certain inclind plane, a body which weighs 50 N requires a force of 35 N to pull it up the incline, If the coefficient of friction is 0.25, find the angle of the incline

A piece of cast iron weighs 75 N in the air and 65 N when suspended in fresh water. Find the relative density of the cast Iron.

A bar 300mm long carries a load of 40, 30, 20, and 50 N at distances of 70, 120, 200 and 240mm respectively from the left end. Neglecting the weight of the bar, calculate the position to place a single support so that the bar will balance.

Calculate the area of a flat plate with the following dimensions length 320mm, ordinates of 0, 35.4mm, 63.2mm, 83.4mm, 96mm, l 02mm, 99.6mm, 86.8mm, 58mm. Using Simpson’s first Rule.

An oil storage tank with triangular shaped ends is arranged horizontally with the apex pointing downward. The tank is l m wide at the top, l. 5m in vertical depth and 2m long. Calculate the depth of oil remaining in the tank (which was originally full) after 500 liters has been used.

A turbine is increased in speed from 2000 to 3600 revs/min. , while it turns 5500 revolutions. Assuming that the rate of increase of speed is uniform, find the acceleration in rad/s2.

A crowbar 2.7m long is used to move an object at one end of the bar. If the force required to move the object is 800N and the maximum effort that could be exerted at the other end of the lever is 100 N. Calculate the max distance of the fulcrum from the end of the bar at which the load is located.

### Test Question Examples #5

The screw of a certain screw jack has a lead of 10mm. An effort of 1 20 N is applied tangentically at the end of a bar having a radius of 250mm. If the efficicncy is 30% calculate
(b) the velocity ratio (V.R.)

Calculate the safe load in KN that can be carried by a stud of 580 mm cross sectional area at the bottom of the thread allowing a safe working stress of 35 MPa. Calculate also the number of these studs required to hold the cylinder cover of a diesel engine where the maximum pressure in the cylinder is 4200 KPa and the dia. Of the cover inside the joint is 300 mm.

A motor car is on the verge of skidding when traveling at 45 KM/hr. on a level road around a curvature of 3Om radius. Find the coefficient of friction between the tires and the road.

A derrick Sm long is attached to an upright pillar and at the top is supported by a horizontal tie 2.6 m long. Calculate the forces In the derrick and the tie when a load of 100 KN is being lifted.

A beam of uniform section is 15 meters long and weighs 4KN. it is simply supported at the left end and at 5 meters from the right end and carries a load of 2, 5, 6 KN at 2, 5, and 12.5 meters respectively from the left end, Find reactions.

The top of a flag staff as viewed from a point on a level ground at some distance from the foot of the staff, and the angle of elevation is 45° 30'. At another point 10m further away from the foot, the shaft top is viewed again, and this time the angle of elevation is 37° 38'. Find the distance from the foot of shaft to the first observation point and also the height of the flag shaft.

The diameters of a wheel and axil are 300mm and 75mm when a body having a mass of 300 Nis beinglifted. The efficiency is 80%. Calculate — (A) The velocity ratio ( V. R.)
(b) the effort required
(d) the useful work done when the load is raised 200mm
(e) the corresponding work done by the effort

A vertical Sluice Gate is 600mm wide by 900mm high and its mass is 367 kg. It covers an inlet from the sea, the bottom of the gate being 5m below water level. Taking the coefficent of friction between the sliding surfaces of the gate and its guides as 0.27, and the density of sea water as l.025g/ml. Find the maximum force to lift the gate.

The right angle triangular place has an angle of 28° 37'. and the length of the hypotenuse is 120mm. Find the lengths of the other two sides and the area of the triangle

### Test Questions Examples #6

A section of a ships deck is composed of 7mm plating having a mass of 5495 kg/m2 of Area It is stiffened by 200 x 8.5mm bulb plate welded to the deck at 1 m intervals, The bulb plate has, a mass of 1 7.6kg/m length. Calculate the mass of a portion of the deck 20m long forward and aft and 12m wide.

A propeller blade from root to top is 2.4 m long. At seven equidistant places, the breadths are: 0.70m, 0.34m, 0.95m, 1.13m 0.91 m, 0.55m and 0.0m. Find the area by Simpsons First Rule.

The surface of a solid sphere is 1 1/2 times the surface area of a smaller sphere and the difference in their volumes is 10 cm3. Find the volume and diameter of the smaller sphere.

An eccentric sheave of uniform thickness is 500mm dia. The hole for the shaft is 125mm dia. and It's centre is l00mm frorm the centre of the sheave. Calculate the positlonof the centre of gravity of the sheave from its geometrical centre.

A uniform beam A—B has a single support 1.7m from “A”. The mass required to balance the beam if 100 kg applied at “A”. if the point of suspension is moved to a point 2 m from A and the mass required to balance the beam is reduced to .50kg. Find the length and the mass of the beam.

A fly wheel is brought to rest from a speed of 300 rpm. if the retardation is uniform at 0.25 rad/s2, Find the time to come to rest, and the number of revs turned during this peroid.

A piece of machinery having a mass of 2 tonne is lifted by a crane hook attached to the middle point of a rope sling as illustrated. The hook is vertically above the centre of gravity of the load and the sling is symmetrically placed as shown. Determine the tension in the tow sides of the sling and examine the effect of shortening the sling.

A body of 200 N mass is to be pulled up a slope which is inclined at 30 degrees to the horizontal. The coefficient of friction between the body and the plane being 0.2. Find force required assuming it to be applied parallel to the plane, and also find the work done in pulling the body a distance of 50 metres up the slope.

Find the number of teeth in the worm wheel of a worm driven screw jack to give a velocity ratio (TMA) of 550 of the worm is single threaded the screw has a pitch of 16mm and the effort wheel is 100mm dia. Assuming an efficiency of 30%, find the effort required to Lift a load of 50 KN

### Test Question Examples #7

Two round bars, each 85mm Dia., are screwed at their ends and scoured together by a cjli cylindrical coupling screwed interrially the depth of the screw thread is 2.5mm, Assuming that the coupling and faces are all the same material, find the outside diameter of the coupling to give equal strength in tension.

A warwick (turnbuckle) screw is used to tighten a guy rope. The right and left hand thread, each have a pitch of 4mm and the effective length of the toggle Is 250mm. Assuming an efficiency of 25%, find the pull in the guy rope when an effort of 90 N is applied.

A length of intermediate shafting is 500mm dia., and has a mass of 22 t. If the coefficient. of friction of the bearing surface is 0.07 calculate the power lost duo to friction when the shaft rotates at 70 RPM.

A barge is being towed along a canal of 4Km/h. The pull in the rope is 300 N and the rope is inclined at an angle of 25% to the direction of motion of the barge. Calculate the work done in 2 minutes.

A barge being towed along a canal by a rope inclined at a 20° direction to the canal, the tension in the rope is 200 N. Calculate the values of the rectangular components of this tension, one component being in the direction of the canal and the other at right angles to the canal bank.

A wheel and axil is carried in horizontal bearings. A cord which is fixed to and wrapped around the axle carries a load on its free end. When the load is allowed to fall from rest, it falls 3 meters in B seconds, if the diameter of the axle is 50mm, find the linear acceleration of the load in m/s2

A ship leaves port and travels at 9 knots. Another ship leaves the same port 6 hours later and ,travelling in the same direction draws alongside the first ship when 259 kilometers from this port. Find the speed of the overtaking ship.

A stone is dropped from a tower I 00m high. Assuming g= 9.81 m/s2 and the air resistance to be negligible, calculate:
(a) the time taken to reach the ground
(b) the velocity of the stone when it hits the ground
(c) the distance which the stone falls during the first 2 seconds.

The load on a rudder is 150 KN and this acts at a center of pressure 1 meter from the center line of a rudder post. The tiller is 2 meters long. If the tiller is moved by a rod 50mm dia., Find the stress (kPa) in the rod.

1. A solid shaft is 300mm diameter, while another of equal diameter has a 130mm diameter holes bored through it. If both are of equal length, made of the same material and subject to equal stress, by what percentage is one stronger than the other? And by what percentage is one heavier than the other?

2. An oil storage tank with triangular shaped ends is arranged horizontally with the appex downward. The tank is 1m wide at the top, 1.5 m in depth, ans 2m long. Calculate the depth of oil remaining in the tank (originally full) after 500 litres has been used.

3. An object is constructed by fitting the base of a cone to a flat side of a hemisphere are 60mm and the height of the cone and the mass of the object if the density of the material is 8400kg/m3.

4. A cylinder and a sphere and base of a cone are all the same diameter, and the height of the cylinder and cone are each equal to the diameter of the sphere. Find the ratio of the volumes of the cylinder and sphere relative to the volume of the cone.

5. The diameter of the base of a hollow cone is 300mm and it perpendicular height is 500mm. It is partly filled with H20 so that when resting on its base the depth of the H20 is 250mm. If the cone is inverted and balanced on its open end, what will be the depth of the H20?

6. A uniform beam A-B has a single support 1.7m from A. The mass required to balance the beam is 100kg applied at A. The mass required to balance the beam is reduced to 50 kg. Find the length and the mass of the beam.

7. An eccentric sheave of uniform thickness is 500mm diameter. The hole for the shaft is 125mm diameter and its center is 100mm from the center of the sheave. Calculate the position of the center of gravity of the sheave from its gravitational center.

8. The pressure on a thrust is 15 tonne and the coefficient of friction is .085. The mean radius of the collar is 200mm and the shaft rotates at 80rpm. Calculate the power lost due to friction.

9. The face of a steam engine slide valve is 150mm by 300mm, and the steam pressure on the back of the valve is 1200kpa. If the coeffecient of friction is .02, find the force required to move the valve.

10. A body lying on an incline which rises 1 in 4 requires a force of 1080N to pull it up the incline and 80N to pull it down. Find the weight of the body and the coeffecient of friction.

11. On a certain incline plane, a body which weighs 50N requires a force of 35N to pull it up the incline. If the coeffecient of friction is .25, find the angle of the incline.

12. A train has a uniform acceleration of .2m/S2. On a straight track. Calculate:
A) the velocity after an interval of 16 seconds of a stand still.
B) the time required to attain a velocity of 50km/hour
C) the distance travelled from stand still until the train attains a velocity to increase of 50km/hour
D) the time taken for the velocity to increase from 30km/hour to 50km/hour, and the distance traveled during this time.

13. A motor car travelling at 50 km/h on dry level surface should stop in 14 metres. Assuming the retardation to be uniform. Calculate:
A) its value
B) the corresponding braking time
C) the distance traveled during the first second after application of the brakes.

14. A stone is dropped from a tower 100m high. Assuming g=9.81 m/s2 and the sir resistance to be negligible, calculate A) the time taken to reach the ground; B) the velocity of the stone when it hits the ground, and ; C) the distance through which the stone falls the first 2 seconds.

15. A flywheel is brought to rest from a speed of 300 rpm. If the retardation is uniform at .25 find the time to come to rest and the number of revs turned during this period.

16. A wheel and axel is carried in horizontal bearings. A cord which is fixed to and wrapped around the axel carries a load to its free end. When the load is allowed to fall from rests, it falls 3 metres in 8 seconds. If the diameter of the axel is 50 mm, find the linear acceleration of the cord in m/s2. And the angular acceleration of the wheel and axel .

17. A motor car is on the verge of skidding when traveling at 48 km/h. On a level road around a curvature of 30m radius. Find the coefficient of friction between the tires and the road.

18. Sea water is pumping through a 50mm diameter pipe to a height of 9m. If the velocity of the water through the pipe is constant at 1.5m/sec. Find the equivalent output power. Find also the input power to the pumps if the efficiency of the system is 0.6. The density of sea water is 1.024g/ml.

19. A rope brake is used to measure the brake power of a small engine, the diameter of the flywheel is 1220mm and diameter of the rope is 25mm. Find the power when the engine is running at 420 rpm, the load on one end of the rope being 267N and the reading of the spring balance is 44.5N.

20. A set of rope pulley with 3 pulleys in each block is used to pull a machine up slids inclined at 20% to horizontal. The mass of the machine is one ton and the coefficient of friction between it and the skid is, 4.The pulley blocks are parallel to the skid and arranged so that the pull on the free end of the ropes is up to the plane. Find the effort required assuming an efficiency of 75%.

21. The effort of a worm wheel chain block is 200mm diameter, the worm is single start and there are 40 teeth in the worm wheel. The load wheel is 125mm diameter and the load is carried by a snatch block on the loop of the lifting chain from the load wheel to the frame work of the machine. If the effort required to lift a load of 6.72kN is 150N, find the efficiency when lifting this load and the V.R. (TMA) of the unit.

22. A hollow cylinder cooling column, 120 mm outside diameter, and 50mm diameter support load of 200kN. Find the compression stress in the material.

23. Calculate the safe load in kN that can be carried by a stud of 580mm2 cross sectional area at the bottom of the thread allowing a safe working stress of 35Mpa. Calculate also the number of these studs required to hold the cylinder cover of a diesel engine where the maximum pressure in the cylinder is 4200 kpa and the diameter of the cover inside the joint is 380mm.

24. Two round bars, each 85mm diameter are screwed at their ends and screwed together by a cylindrical coupling thread is 2.5mm. Assuming that the coupling and faces are all the same material find the outside diameter of the coupling to give equal strength in tension.

25. In hand driven double purchase winch, the radius of the crank handle is 300mm, the load drum is 200mm diameter and the rope is 25mm diameter. The driving wheels have 30 and 25 teeth and the followers have 90 and 125 teeth. Find A) the velocity ratio, B) efficiency hen lifting a mass of 1000kg if the efoort required is 350N..

26. Find the number of teeth in the worm wheel of a worm driver screw jack to gaive a velocity ratio (TMA) of 550 if the worm rowing 6 thread. The screw has a pitch of 16mm and this effort which is 100 mm diameter. Assuming efficiency of 30%, find the effort required to lift a load of 50 kN.

27. Sea water is pumping through a 50mm diameter pipe to a height of 9m. If the velocity of the water through the pipe is constant at 1.5m/sec. Find the equivalent output power. Find also the input power to the pumps if the efficiency of the system is 0.6. The density of sea water is 1.024 g/ml.

28. A line shafting transmits 4000KW when rotating at 74rpm. Individual lengths of shafts are connected together by couplings having 9 bolts 90 mm diam. , located at the radius of 330mm from the shaft axis. Calculate the mean shear stress in the bolt.

29. Calculate the relative density of the mixture formed when 10m3 of a liquid or relative density of 1.31 is mixed with 8m3 of liquid of relative density .98.

30. A pump lever is 43mm deep. 32mm thick and the distance from the pump links to the fulcrum of the lever is 743mm. If the tensile strength of the beam is 430Mpa and allowing a factor of 5, calculate the load in the pump lever.

31. A force of 4300N acting at the end of a spanner 50cm long can twist off a 30mm diameter. Stud. Calculate the torque required to twist off a stud having a 45mmm diam.

32. A circumferential seam of a cylindrical pressure vessel is a double riveted lap joint. The rivets are 33mm diam. And their shearing strength is 345Mpa. The plates are 30mm thick and the tensile strength is 435 Mpa. Find A) the pitch of the rivets to give a seam strength efficiency not less than 55 % and B) the pitch to give maximum seam strength.

33. A rectangular cantiler beam is 1.6 m long and 85 mm thick. It supports a load of 9kN on its free end. Calculate the depth of the beam for the maximum stress on the material is to be 48Mpa.

34. A straight length of a steam pipe 180mm outside diameter and 7mm thick conects the bulkhead stop valve with the engine stop valve. If it is fitted at a temperature of 16 C , find A) the stress in the pipe when heated to 200C by steam passing through if no allowance were given for expansion and B) the thrust on the stop valve.

35. The shell plates of a boiler 4.5 in diameter are 42mm thick and the inside strength of the material is 495Mpa. The efficiency of the longitutal seam is 85% and that of the circumferential seam is 50%. Find the working pressure allowing a factor of safety of 5.

36. A ship's speed in still water is 16 knots.  The ship travels 15 miles with the current and 15 miles against the current.  If the time traveled was 1 hour 56 minutes what was the speed of the current?

37. A plank weighs 65 kg.  With an additional 30kg added to the plank it becomes just awash in a tank containing oil at a relative density of 0.95. What is the relative density of the plank?