Mechanics Tutorial: Solving Problems with Acceleration and Velocity

[robwat22]

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?

 

[daniel_i_l]

People won't like to help you if you don't show some work!

 

[rahuldandekar]

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 . IT has a superb guide to solving them.

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

 

[robwat22]

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

 

[TolsePhy]

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.