How to solve the problem on Mechanics? (guidelines)

1. Write down all physical quantities of the problem, with their dimensions and values in SI.

2. Be sure to make a pattern (large!) or circuit of the phenomenon, which shows the designation of values related to the problem. Sometimes it is useful to make a series of drawings for the different stages of the process.

3. How do you find this phenomenon from different frames of reference? Select the most suitable.

4. What happens with the different types of energy in this phenomenon? How to write the energy balance?

5. Can you use the conservation laws to solve the problem? What is it?

6. What physical laws describe this phenomenon?

7. Always solve the problem in a general way and only after obtaining an analytical expression for an answer, a numerical calculation must be done.

8. Be sure to analyze the answer:

   1. in dimension;

   2. in extreme cases;

   3. the manifestation of symmetry;

   4. the plausibility of the numerical value.

9. After solving the problem specify again the physical laws that have been used to solve the problem. You must remember well these laws!

10. Ask yourself the question: What is new did you learn by solving this problem?

Tasks for home work on mechanics of 2015

Special assignment # 2

1. A motorboat going downstream overcame a raft at a point A; later it turned back and after some time passed the raft at a distance l = 6.0 km from the point A. Find the flow velocity assuming the duty of the engine to be constant.

2. A point traversed half the distance with a velocity . The remaining part of the distance was covered with velocity for half the time, and with velocity for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion.

1.4. A point moves rectilinearly in one direction. Fig. 1.1 shows

­the distance s traversed by the point as a function of the time t.

Using the plot find:

(a) the average velocity of the point during the time of motion;

(h) the maximum velocity;

(c) the time moment to at which the instantaneous velocity is equal to the mean velocity averaged over the first to seconds.

1.8. Two boats, A and B, move away from a buoy anchored at the middle of a river along the mutually perpendicular straight lines: the boat A along the river, and the boat B across the river. Having moved off an equal distance from the buoy the boats returned. Find the ratio of times of motion of boats if the velocity of each boat with respect to water is times greater than the stream velocity.

1.9. A boat moves relative to water with a velocity which is times less than the river flow velocity. At what angle to the stream direction must the boat move to minimize drifting?

1.11. Two particles move in a uniform gravitational field with an acceleration g. At the initial moment the particles were located at one point and moved with velocities and horizontally in opposite directions. Find the distance between the particles at the moment when their velocity vectors become mutually perpendicular.