Urgent Dynamics and Mechanics Help: Difficult Energy, Work, and Power Questions

[Scarface_Joker]

Hi guys - this is going to seem pretty demanding for a first post but I am desperate.

I have a series of 11 questions here spanning Energy/Work and Power, Elasticity and Coplanar Forces that I need masses of help with. I'm finding them to be the most difficult questions of any subject I've ever had to do, I don't know whether you guys will feel the same or indeed find them easy.

Just assume I haven't gotten anywhere, which for most of the questions is true. I'm in need of guidlines on how to solve the whole problem, complete solutions would be an absolute godsend.

I'm really sorry for such a laborous post, but I am almost at the point of a breakdown.

Questions

1.Find the power required to raise water 3 m vertically from a tank and
discharge it through a nozzle of cross-sectional area 0.0003 m^2 at a speed of 10 m/s.

2.A mass of 1 kg rests on a horizontal table. It is connected by a taut, light, inextensible string passing over a smooth fixed pulley, at the edge of the table,to another mass of 3 kg hanging vertically. The 3 kg mass is at a height of 0.5 metres above an inelastic floor when the system is released from rest. There is also a frictional resistance to the motion from the table of 0.5 N. Determinethe total work done by the frictional force, assuming that the 1 kg mass stops before reaching the pulley.

3.A mass of 5 kg is attached to one end of an elastic string of natural length 2 m and modulus of elasticity 10g N, the other end being attached to a fixed point A. The mass is held at A and allowed to fall vertically. How far below A will it first come instantaneously to rest, assuming that there are no obstructions in its path?

4.One end of an elastic string is fixed to a point A on a smooth horizontal table.The other end is attached to a heavy particle P of mass m. The particle is pulled away from A until AP = 1.5l, where l is the natural length of the string, and is released. If the string's modulus of elasticity is mg find the velocity of the particle when the string reaches its natural length.

5.A mass is suspended from a point O by an elastic string of natural length l so that the length of the string is 5l/3. Show that if the mass is allowed to fall freely from O the greatest length of the string during the ensuing motion is 3l.

6.An elastic string has natural length a and modulus of elasticity mg. One end is attached to a point O and the other to a particle of mass m. If the particle is held at a distance 4a below O and then released, find the height above O to which it will rise.

7.A uniform rod AB of length 2a weighs 10N. It is freely hinged to a vertical
wall at A and is kept in equilibrium by a string CB of length 2a (C vertically
above A) such that AB is inclined at 30° to the horizontal. Find the magnitudes and directions of the tension in CB and the reaction at A.

8.Forces of 3 , 4 and 6 Newtons act at 30°, 60° and 120° respectively to the horizontal. Find the horizontal and vertical components of the resultant and hence its magnitude and direction.

9.Forces of 1, 2, 3 and 4 Newtons act along the sides of a regular hexagon
ABCDEF of side a in the directions BA, CD, ED and FA respectively. Find
the magnitude and direction (with respect to ED) of the resultant of this systemand also determine where it cuts DE.

10.A uniform beam AB of length 6 m and weight 11 N rests horizontally on two supports C and D, where AC = 1 m and DB = 2 m. Weights of 6 N and 7 N are hung from the end points A and B respectively. Calculate the reactions at each support. What extra force must be applied at B in order to cause the beam to just lift off the support at C?

 

[Astronuc]

It is customary for the student (poster) to show his/her work.

Please try to write the equations for each problem. Presumably, the physics and related equations are discussed in one's textbook or covered in class.

As a policy we do not solve problems in their entirety. We do work through problems with students, but students must do their own work.

Also, please check the tutorial sections.

 

[quicknote]

11.A car of mass 1500 kg accelerates at 2.4 m/s^2 on a straight level road. Its
engine propels it at full power for 20 seconds, then the engine is turned off
and the car continues to move without resistance. Find:

a) the final velocity of the car at the end of the 20 seconds

b) the total distance travelled in the 20 seconds

c) the average power developed by the engine during the acceleration

Dear student,

I understand that these questions may seem overwhelming and difficult, but I would suggest breaking them down into smaller parts and approaching them systematically. Here are some general guidelines for solving problems in dynamics and mechanics:

1. Draw a clear and accurate diagram of the system and label all the given information.

2. Identify the relevant equations and principles that apply to the problem. For example, for question 1, you will need to use the equation P = Fv to calculate power.

3. Make sure to use consistent units throughout your calculations.

4. For questions involving elastic strings, use Hooke's law (F = kx) to relate the force, displacement, and modulus of elasticity.

5. For questions involving forces at angles, use vector addition to find the resultant force.

6. Remember to take into account any resistive forces, such as friction or air resistance.

7. Check your units and answer to make sure they make sense. For example, power should be measured in watts (W) and force in newtons (N).

I would also recommend practicing similar problems and seeking help from a teacher or tutor if needed. Do not hesitate to ask for clarification or additional guidance if you are still struggling with these questions.

I hope these guidelines help you in solving these challenging questions. Remember to take breaks and stay calm, as getting overwhelmed can make it harder to solve the problems. Good luck!