Mechanics Tutorial: Solving Problems with Acceleration and Velocity

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In summary, the conversation discusses various mechanics problems involving acceleration, velocity, and collisions between particles. The first problem involves two cars with different accelerations and asks for the time and velocity when they first meet and when they meet again. The second problem involves particles connected by a string on an inclined plane and requires using conservation of energy. The third problem involves a constant force applied to a particle on an inclined plane and asks for the velocity and work done after a certain time. The final problem involves two particles on a smooth surface and a vertical wall, and requires considering the conservation of momentum and using the coefficients of restitution. The conversation also emphasizes the importance of showing work in order to receive help.
  • #1
robwat22
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MECHANICS - Help Needed!

Hi guys, I've got this tutorial sheet to do, and I am pretty stuck on it, i don't really need the answers i can do them myself i just need somewhere to start on the questions and and idea of what to do. Help much appreciated!

1. A car starts from rest and moves along a straight road with acceleration 9ms-2. After 5 seconds another car starts from rest at the same point and moves along the same road with acceleration 16ms-2.
• How long after the first car starts will the second car catch it up?
• What are the velocities of the two cars when they first meet?
• The second car now stops accelerating and travels at constant velocity. How many more seconds after the first meeting will they meet again?

2. Particle A of mass 2 kg and particle B of mass 5 kg are connected by a light inextensible string, which passes over a smooth fixed pulley at the top of a smooth plane inclined at 30° to the horizontal. A is on the plane and B is hanging vertically. At t = 0 both particles are moving with speed 4ms-1 with A moving downwards and B moving upwards and A is 1 m from the top of the plane.
• Calculate when A reaches the top of the plane.

3. A constant horizontal force of 30 N is applied to a particle of mass 5 kg which moves up a smooth plane inclined at 20° to the horizontal. The particle is initially at rest. Find the velocity and the work done by the force after t seconds.

4. Particle A has mass 5kg and particle B has mass 1kg. They lie on a smooth horizontal surface and the line joining them is normal to a vertical wall with B closer to the wall. The coefficient of restitution between the two particles is Ep = 0.8 and the coefficient of restitution between B and the wall is Ew = 0.5. Initially A is at rest and B is moving towards A at a speed of 2m/s. B collides first with A and then with the wall.
• Will it collide with A again?
• What is the final velocity of A?
 
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  • #2
People won't like to help you if you don't show some work!
 
  • #3
The kinematics problems are easy, you need to use the three kinematical equations, that's all.

For the mechanics problems, you should refer to http://www.csupomona.edu/~ajm/materials/n2.html [Broken]. IT has a superb guide to solving them.

But, yes, show us some work if you want our help on the specific problems.
:)
 
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  • #4
Q1

So far I've got:

for car A: a= 9, u=0, v=?, t=(?+5), s=?
for car B: a= 16, u=0, v=?, t=?, s=?

Find distance car A travels after 5 seconds, ie
s = ut + 1/2 * a * t^2
s = 0*5 + 1/2*9*5^2 = 112.5 m
I know that sb = sa + 112.5 m

Find velocity of car A after 5 seconds,
v^2 = u^2 + 2as
v^2 = 0^2 + 2*9*112.5
v^2 = 2000 => v=SQRT[2000] => 44.72 ms-1

Now i need to find the time it takes for car B to reach car A if it starts 5 seconds after car A. So i need to find t and most probably v & s.

Im thinking the following:
using: s = ut + 1/2 * a * t^2 in sb = sa + 112.5 m
so,0.5*16*(t)^2 = 0.5*9*(t+5)^2 + 112.5

If I get t I should be able to find everything else for now.

Thanks, rob
 
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  • #5
1. when the second car got the same speed with the first one, it can catch up the first one. by using v=u+at, you get all the things.

2. by conservation of energy: KEi+PEi=KEf+PEf, you can get the distance traveled by A along the inclined plane just before it came to instantaneous rest. then, the problem can be done as if two particles are at rest initally.

3. by F=ma, a can be found, then by v=u+at and s=u+1/2at^2, done!

4. for such problem, recalling the conservation of momentum and thinking about what do the system include.
 

1. What is mechanics?

Mechanics is the branch of physics that deals with the study of motion and forces on objects. It involves understanding how objects move and why they move in certain ways.

2. What kind of help is available for mechanics?

There are many resources available for mechanics help, including textbooks, online tutorials, and private tutors. You can also seek help from fellow students or professors.

3. What topics are covered in mechanics?

Mechanics covers a wide range of topics, including kinematics, dynamics, energy, momentum, and rotational motion. It also includes concepts like Newton's laws of motion, work and energy, and conservation of momentum.

4. How can I improve my understanding of mechanics?

To improve your understanding of mechanics, it is important to practice solving problems and to review concepts regularly. You can also try visual aids, such as diagrams or animations, to help you understand complex concepts.

5. Why is mechanics important?

Mechanics is important because it helps us understand the physical world around us. It is the foundation of many other branches of physics, and its principles are used in many fields, from engineering to sports to space exploration.

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