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I've been bottling them up whilst doing other questions for a while now, but I just need to know how to do them now! Can anybody assist me?
1:A particle P, of mass 2kg, lies on a rough plane inclined at an angle of 30degrees to the horizontal. A force H, whose line of action is parallel to the line of greatest slope of the plane, is applied to the particle as shown in Figure 2. The coefficient of friction between the particle and the plane is 1/root3.
Given that the particle is on the point of moving up the plane,
a) show that the ratio of the magnitude of the frictional foce to the magnitude of H is equal to 1:2
The force H is now removed but P remains at rest.
b) Use the principle of friction to explain how this is possible.
2:A car of mass 1.25 tonnes tows a caravan of mass 0.75 tonnes along a straight, level road. The total resistance to motion experienced by the car and the caravan is 1200 N. The car and caravan accelerate uniformly from rest to 25 ms^-1 in 20 seconds.
a) Calculate the driving force produced by the car's engine.
Given that the resistance to motion experienced by the car and by the caravan are in the same ratio as their masses,
b) find these resistances and the tension in the towbar.
When the car and caravan are travelling at a steady speef of 25ms^-1, the towbar snaps. Assuming that the caravan experiences the same resistive force as before,
c) Calculate the distance travelled by the caravan before it comes to rest.
3:
A cyclist and his bicycle have a combined mass of 78kg. While riding on level ground and using his greatest driving force, he is able to accelerate uniformly from rest to 10 ms^1 in 15 seconds against constant resistive forces that total 60N.
a) Show that her maximum driving force is 112N.
The cyclist begins to ascend a hill, inclined at an angle Z to the horizontal, riding with her maximum driving force and against the same resistive forces. In this case, he is able to maintain a steady speed.
b) Find the angle Z,giving your answer to the nearest degree.
c) Comment on the assumption that the resistive force remains constant
- in the case when the cyclist is accelerating.
- in the case when she is maintaining a steady speed.
4:
Two particles, P and Q, of mass 2kg and 1.5kg respectively are at rest on a smooth, horizontal surface. They are connected by a light, inelastic string which is intially slack. Particle P is projected away from Q with a speed of 7ms^1.
a) Find the common speed of the particles after the string becomes taut.
b) Calculate the impulse in the string when it jerks tight.
