Vector Quantities - General Physics - Solved Exam, Exams of Physics

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2003 Question 6 Give the difference between vector quantities and scalar quantities and give one example of each. A vector has both magnitude and direction whereas a scalar has magnitude only. (i) Describe an experiment to find the resultant of two vectors.

1. Attach three Newton Balances to a knot in a piece of thread.
2. Adjust the size and direction of the three forces until the knot in the thread remains at rest.
3. Read the forces and note the angles.
4. The resultant of any two of the forces can now be shown to be equal to the magnitude and direction of the third force.

(ii) A cyclist travels from A to B along the arc of a circle of radius 25 m as shown. Calculate the distance travelled by the cyclist. The displacement is equivalent to one quarter of the circumference of a circle = 2πr/4 = 25π/ = 12.5π = 39.3 m. (iii) Calculate the displacement undergone by the cyclist. Using Pythagoras: x^2 = 25^2 + 25^2  x = 35.3 m. Direction is NW (iv) A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900 N. The ramp makes an angle of 10o^ with the horizontal. Calculate the force required to keep the wheelchair moving at a constant speed up the ramp. (You may ignore the effects of friction.) If the wheelchair is moving at constant speed then the force up must equal the force down. So to calculate the size of the force up, we just need to calculate the force down: F = mgSinϑ = 900 Sin 10o = 156.3 N (v) The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her 10 s to travel up the ramp. Power = work/time Work = Force × displacement = 156.3 × 5 = 780 J Power = 780/10 = 78 W

2003 Question 12 (a) (i) State Newton’s second law of motion. Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force. (ii) A skydiver falls from an aircraft that is flying horizontally. He reaches a constant speed of 50 m s–1^ after falling through a height of 1500 m. Calculate the average vertical acceleration of the skydiver. v 2 = u^2 +2as (50)^2 = 0 + 2(a)(1500) a = 0.83 m s- (iii) If the mass of the skydiver is 90 kg, what is the magnitude and direction of the average resultant force acting on him? F = ma = 90 × 0.83 = 75 N Down (iv) Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed. Weight acting down on diagram Air resistance / friction / buoyancy acting up on diagram Air resistance = weight, therefore resultant force = 0 Therefore acceleration = 0