UNIVERSITY of PLYMOUTH

 

MECH115: Engineering Science 1

 

Tutorial examples: - Forces and Moments                           [Use g = 9.81 m/s² where required]

 

 


      Sign convention:                  +ve

                                                                                               

 

 

 

  1. Three forces of magnitude 100, 150 and 185 N act at a point in directions 0, 65 & 95 respectively. Using graphical methods find the magnitude and direction of the resultant.  [352.4 N at 65.3º]

 

  1. Four forces of magnitude 3, 12, 15 and 24 kN act at a point in directions 10º, 100º, 240º and 310º respectively. Using graphical methods find the magnitude and direction of the resultant. [21 kN at 294.8º]

 

  1. Repeat the solutions of Questions 1 and 2 using a spreadsheet. How accurate was your graphical solution compared to the spreadsheet solution?

 

  1. A motor car has a mass of 1040 kg and is parked on a ramp sloping 25º to the horizontal. Find the force components of its weight in the directions parallel and at right angles to the ramp surface. [4312 N, 9247 N]

 

  1. A barge is pulled along a canal by a horse walking along the tow path where the tow rope forms an angle of 12º to the longitudinal axis of the barge. If the tension in the rope is 950N what is the force tending to pull the barge toward the bank. [198 N]

 

  1. In Question 5, if the tow rope is attached to the front of the barge, and the barge itself is 20m long, what is the moment of the towing force about the centre of the barge tending to rotate it toward the bank? In practice, how is the side force and moment counteracted? [1,975 Nm]

 

  1. Older cars used to be started using a crank handle. If the crank arm of a crank handle is 170mm, and an upwards force applied is 600N at right angles to the crank arm, what torque is being applied to turn the engine? What force acts to lift the front of the car? [102 Nm]

 

  1. In the figure below find the moment of the force applied at A, (i) about the mid-point, and   (ii) about the support point B, of the cantilever AB. [-362 kNm, -725 kNm]

 

 

 

 

 

 

 

 

 

 

 

 

 


  1. If the weight of the cantilever beam in Question 8 was 50 kN, by what percentage does the moment at B and at the mid-point increase? [ 4.3% (B), 1.7 % (mid-point)]

 

 

  1.  The diagram below shows an equal arm control quadrant with forces applied to it as shown.
     Find the torque transmitted by its actuating shaft A. [3.78 Nm]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


  1. For Question 10, find also the resultant force acting at A, and hence find the magnitude and direction of the force that needs to be applied at B to ensure that the shaft A transmits a torque only with no lateral force applied a A. Find the magnitude of this torque.                     [47.2 N at 95.2º, 2.41 Nm]

 

 

 

115tut_forces&moments