(I)Explain Why It Is Necessary to Regard Forces a and C As Resultant Forces
5. N06/III (part)
A car traveling along a flat road may be considered to have three forces acting on it. These are represented in the figure below.
(a)
(i)Explain why it is necessary to regard forces A and C as resultant forces.
(ii)Force A has a magnitude 8200 N and is at an angle of 28o to the vertical. Force B is horizontal and has a magnitude 1500 N.
Calculate
- the weight and the mass of the car.
- the resultant force on the car.
- the acceleration of the car.
(iii)For the car, motion is impossible without friction. Discuss what is meant by friction and the direction in which it acts on the car. In your answer, suggest another example where friction is useful.
(b) Describe a situation in which motion is produced without friction being required.
4. J98/III/1
A cyclist moves down a road inclined at an angle of 6.8° without pedaling. The total weight of the cyclist and the bicycle is 760 N.
(a) A graph of his velocity v is plotted against time t.
(i) Using the graph, determine the initial acceleration of the cyclist.
(ii)1. Using your answer in (a)(i), calculate the accelerating force acting on the cycle and cyclist time t = 0.
2. Hence, determine the resistive force acting on the cycle and cyclist at time t = 0.
(iii)State the magnitude of the resistive forceacting on the cycle and cyclist at time t=30 s
(iv) Suggest why the total resistive force has changed between time t = 0 and t = 30 s.
[0.70 m s-2, 54 N, 36 N, 90 N]
(b) The cycle is serviced in order to reduce friction and then the journey down the slope is repeated. State and explain what change, if any, will occur in the maximum velocity of the cycle down the slope.
(c) Having descended the slope, the cyclist travels along a horizontal straight section of the road at a speed 7.0 m s-1. When the brakes are applied, the cyclist takes 3.5 s to come to rest.
(i) Calculate the average force opposing motion during the time that the brakes are applied, assuming the cyclist is not pedaling. [160 N]
(ii) Comment on whether the brakes are efficient enough to bring the cycle to a halt when on the inclined road.
6. A helicopter has blades of diameter 5.0 m is hovering above the ground at a particular instance. Its blades are rotating in such a way that they are pushing air downwards at a speed of 18 m s-1. The density of the surrounding air can be taken as 1.02 kg m-3.
Calculate the upward force acting on the blades. [6500 N]
7. A toy rocket consists of a plastic bottle which is partially filled with water. The space above the water contains compressed air.
At one instant during the flight of the rocket, water of density is forced through the nozzle of radius r at speed v relative to the nozzle. Determine in terms of , r and v,
(i) the mass of water ejected per unit time from the nozzle
(ii) the rate of change of momentum of the water
Hence show that the accelerating force F acting on the rocket is given by the expression
F = r2 v2 – mg, where m is the mass of the rocket and its contents at the instant considered.
8. N91/I/5
When a man is standing in an ascending lift, the magnitude of the force exerted on the man’s feet by the floor is always
Aequal to the magnitude of his weight
Bless than the magnitude of his weight
Cgreater than what it would be in a stationary lift
Dequal to what it would be in a stationary lift
Eequal to the magnitude of the force exerted on the lift floor by his feet
- NJC/2007/Prelim
Two blocks, X and Y, of masses m and 2m respectively, are accelerated along a smooth horizontal surface by a force F applied to block X, and resisted by force ½ F applied to block Y, as shown in the diagram below.
What is the magnitude of the force exerted by block Y on block X during the acceleration?
1