object sliding down horizontal, frictionless slope, crossing horizontal surface

kapowa

1. The problem statement, all variables and given/known data

block A slides down an 8 m frictionless ramp that is curved 30 degrees above the horizontal.
it then crosses a 4m surface that has a coefficient of friction that is 0.20.
it then hits a ball and continues moving at 3 m/s.

the ball is suspended from a string, kinda like a pendulum. You have to find out how high the ball goes.

mass of block a is 5kg
mass of ball a is 2.5 kg

2. Relevant equations
Ek = 0.5mv^2
Eg = mgh
vf^2 = vi^2 + 2ad
Ff= μFn
p=mv


3. The attempt at a solution
to find the speed of the block after sliding down the ramp, i simply used some the sin function to determine the vertical distance the block moved down the ramp and then used the formula E(gravity)= mgh to find out the energy it had at the top of the ramp. I then converted this energy to kinetic energy (formula E(kinetic) = 0.5mv^2) which it would have gained at the bottom of the ramp and found the speed to be around 8.85 m/s.

then to find the speed after the block crossed the 4m distance, i used the the formula for friction. To find the normal force, i used Fg = mg cuz gravity and normal force are the same in magnitude, and put this in the F(friction) = μFn formula and then got the negative acceleration and plugged that into the kinematics formula above to get a speed of about 7.9 m/s after crossing the 4m surface.

then i used momentum to figure out the height of the ball in the pendulum. Before the collision the momentum was mass of block (5 kg) times speed (abt 7.9 m/s). I setup the formula for the collison like this

momentum before = 5kg x (approx. 7.9m/s)

after the collision the block was moving at 3 m/s
momentum after = 5 kg x (3 m/s) + 2.5(v(of ball a))

since momentum is conserved i solved the equation to find v of ball a which was about 9 m/s. i then used the kinetic energy formula to find the energy at that point right after the collision. At this point kinetic energy was at a max and potential energy was at a minimum. I then converted the energy to potential which would have happened when the pendulum swung to one side. I used the formula Ep = mgh to finally find the height of the ball which i got to be around 5meters (4.9 something)

I am not sure if this was correct way of doing it. I saw a similar question elsewhere and saw that the answers were somewhat different. i wanted to know if i was right in the way i did it, the asnwer did seem reasonable to me.

technician

I have not checked any of your maths calculation but I cannot find anything wrong with your method

kapowa

Okay, thanks a lot. I just wanted to know if my reasoning was correct. The numbers don't really matter that much. It was just a practice question.

ehild

It looks correct. But keep at least 3 significant digits in the intermediate results .

ehild