Exam Questions - Test 1 Flashcards
Q1) A wing screw is tightened using a thumb and finger. The thumb and finger each apply a force F as shown in Figure 2
(https://cdn.discordapp.com/attachments/860926934221062177/971784109561110548/IMG_6237.jpg)
(a) Explain why the pair of forces shown in Figure 2 is a couple
(b) The perpendicular distance x between the lines of action of the force is 3.2 cm as shown in Figure 2. Calculate the force F required to produce a couple of 1.2Nm
(a) Explain why the pair of forces shown in Figure 2 is a couple
They are moving in opposite directions with equal force
(b) The perpendicular distance x between the lines of action of the force is 3.2 cm as shown in Figure 2. Calculate the force F required to produce a couple of 1.2Nm
3.2cm = 0.032m
1.2/0.032 = 37.5
Force = 37.5N
Q2) (a) State the principle of moments
(b) Figure 1 shows a uniform beam, with a length of 3.2m and a mass of 27kg. The beam is places=d with one end and against the bottom of a wall at X. A person holds the beam at 35° to the horizontal by applying a force F to the beam’s other end. F is applied at right angles to the beam.
(https: //cdn.discordapp.com/attachments/860926934221062177/971785106937233470/IMG_6238.jpg)
Determine F by taking moments about X.
(a) State the principle of moments
In equilibrium, the sum of the moments clockwise is equal to the sum of the moments anticlockwise
(b) Determine F by taking moments about X.
Q3) A river flows from west to east. The velocity of the current in the river varies from 0.20m/s near the banks to a maximum of 0.65m/s in the middle of the river, as shown in Figure 1. The current is always parallel to the bank
(https://cdn.discordapp.com/attachments/860926934221062177/971792095910170634/IMG_6239.jpg)
A girl swims from A and aims due north. Her speed relative to the water is a constant of 1.1 m/s.
(a) Show that the magnitude of the girl’s maximum resultant velocity is approximately 1.3m/s as she swims across the river
(b) On different occasions, the girl swims in the river at a speed of 0.9m/s relative to the water and in a variety of directions. State the magnitude and direction of the minimum possible resultant velocity that the girl can have
(a) Show that the magnitude of the girl’s maximum resultant velocity is approximately 1.3m/s as she swims across the river
√1.1^2 + 0.65^2 = 1.277 (1.3m/s)
(b) On different occasions, the girl swims in the river at a speed of 0.9m/s relative to the water and in a variety of directions. State the magnitude and direction of the minimum possible resultant velocity that the girl can have
0. 9 - 0.65 = 0.25m/s
Q4) Figure 2 shows a gymnast standing in equilibrium on a uniform beam, 3.0m from one end.
(https://cdn.discordapp.com/attachments/860926934221062177/971792095566241822/IMG_6240.jpg)
The beam is 5.0m long and supports R and S are 0.5m from each end. The weight of the beam is 700N. The gymnast has a weight of 470N.
Fs is the Force exerted by S on the beam.
By taking moments about X, Calculate the magnitude of Fs.
By taking moments about X, Calculate the magnitude of Fs.
Q5) Figure 1 shows the mast of a sailing boat. A uniform horizontal beam PQ is attached by a pivot to the mast at Q. The beam is supported by a light inextensible rope attached to the top of the mast and to the free end of the beam at P.
The tension in the rope is T
(https: //cdn.discordapp.com/attachments/860926934221062177/971804246381064213/IMG_6246.jpg)
(a) The mass of the beam is 12kg. Calculate T by taking moments about Q
(b) The end of the beam is now raised by shortening the rope until it makes an angle of 90°to the beam as shown in Figure 2
(https: //cdn.discordapp.com/attachments/860926934221062177/971804246645309542/IMG_6245.jpg)
The magnitude of T varies as P is raised. Explain the variation in the magnitude of T. Calculations are not required
(a) The mass of the beam is 12kg. Calculate T by taking moments about Q
(b) Explain the variation in the magnitude of T. Calculations are not required
As the beam is raised the centre of mass moves closer to the pivot. As the beam moves closer to the pivot the moment becomes smaller as it has a consistent force and a smaller distance. The P distance for T increases so moment due to D increases, As T moment increases and moment decreases tension decreases
Q6) Figure 2 shows a rock climber abseiling down a cliff. At the instant shown the climber is stationary and in equilibrium. The force exerted by the cliff on the climber’s feet is Fr. The other forces acting on the climber are:
tension in the rope T = 610N at 20° to the vertical
climber’s weight W = 590N
(https://cdn.discordapp.com/attachments/860926934221062177/971804247098282014/IMG_6244.jpg)
Calculate the vertical component of Fr
Q6) Calculate the vertical component of Fr
590 - (Cos(20) * 610) = 17N
Q7) Figure 2 shows an aircraft That is descending. The horizontal and vertical components of velocity are constant. The thrust T and the weight W are shown. The lengths of the arrows indicate the magnitudes of the forces. There are no resultant moments on the aircraft
(https://cdn.discordapp.com/attachments/860926934221062177/971804247404458054/IMG_6241.jpg)
Draw and label on Figure 2 arrows of suitable lengths top represent the lift and the drag on the aircraft
Q7) Draw and label in Figure 2 arrows of suitable lengths to represent the lift and the drag on the aircraft
(https://cdn.discordapp.com/attachments/860926934221062177/971804247404458054/IMG_6241.jpg)
Q8) Figure 8 shows a section of a suspension bridge. The bridge deck is supported by a single cable attached to a vertical tower
(https://cdn.discordapp.com/attachments/860926934221062177/971804247714828328/IMG_6243.jpg)
Figure 9 is an enlarged view of the cable and the top of the tower. The cable makes an angle of 40° to the horizontal where it meets the tower. Then tension T in each section of the cable is 1.2 *10^8N The weight of the cable is negligible.
(https: //cdn.discordapp.com/attachments/860926934221062177/971804247962320896/IMG_6242.jpg)
(a) Calculate the magnitude of the resultant force exerted on the tower by the cable
(b) The mass of the tower is 7.1 * 10^6 kg. Calculate the magnitude of the reaction R of the ground on the use of the tower
