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A tuning fork is struck once and oscillates in simple harmonic motion at a
frequency of 642 Hz and the tip of each prong moves 2.5 mm to either side of
the centre.
i) Calculate the maximum velocity of one of the prong’s tip in mms-1. [ANS = 10,085mms-1]
ii) Find the maximum acceleration of one of the tip of the prongs in mms-2.
[ANS =4.07 X 107 mms-2]
A small fly on mass 0.25 g is caught in a spider’s web. The web oscillates predominantly with a frequency of 4.0 Hz.
a) What is the value of the effective spring stiffness constant k for the web? [ANS = 0.16 N m-1]
b) At what frequency would you expect the web to oscillate if an insect of mass 0.50 g were trapped? [ANS = 2.8 Hz]
Estimate the stiffness (k) of a spring in a child’s pogo stick if the child has a mass of 35 kg and bounces once every 2.0 seconds. [ANS = 350 N m-1]
Four objects are situated along the y axis as follows: a 2.08kg object is at 2.90 m,a 3.03kg object is at 2.40m,a 2.56 kg object is at the origin,and a 4.05 kg object is at 0.508m.Where is the centre of mass of these objects?
x=
y=
This question is about forces and moments of forces.
a. (I) Define the moment of a force about a point
(II) State the law of moments as a condition for equilibrium
b. A crane has a jib (AC) of mass 2500kg pivoted at A.
The jib is supported by a horizontal cable BC. The centre of mass of the jib its at D. The dimensions are as shown on the diagram.
(I) Make a sketch copy of the diagram and on it draw three arrows to represent the three forces acting on the jib.
(ii) Calculate the tension in the cable BC.
C. The end of the jib C is raised by shortening BC. Explain whether the tension in BC will increase or decrease.
Three branches, possessing a resistance of 50ohm, an inductance of 0.15H and a capacitor of 100µF respectively, are connected in parallel across a 100V, 50Hz supply. Calculate
a) The current in each branch
b) The supply current
- c) The phase angle between the supply current and the supply voltage.
How tall is the building if a ball is thrown horizontally with a velocity of 22.2 m/s from the roof of the building and lands 36 m from the base of the building?
A bird flies 7km on a bearing of 40degress. How far north and east of its starting point is its final position?
SA1. A pebble is projected vertically upward using a sling shot at a velocity of 50.0 m/s. What is its velocity at a height of 2.0 m?
SA2. At what height of the flight of the pebble in SA1 shall it have a velocity of 12.0 m/s?
SA3. How long shall the pebble in SA1 attain a velocity of 0.0 m/s?
SA4. Where shall the pebble in SA1 be located 4.0 seconds after it was launched?
SA5. How far shall the pebble in SA1 be from its point of origin at the time described in SA4?
SA6. A ball is projected vertically upward at a velocity of 15.0 m/s. At what position shall it be located at a velocity of – 10.0 m/s?
A chopper drops boxes of relief goods to a group of people stranded in an island. The goods were released 20.0 m above the sea and landed 40.0 m from a point exactly below where the goods were released. What was the velocity of the goods when they were released? What was the velocity of the chopper?
