• Support PF! Buy your school textbooks, materials and every day products Here!

Dynamics - Relative Motion Help?

  • Thread starter Khamul
  • Start date
  • #1
24
0

Homework Statement


Conveyor belt A, which forms a 20° angle with the horizontal, moves at a constant speed of 4 ft/s and is used to load an airplane. Knowing that a worker tosses duffel bag B with an initial velocity of 2.5 ft/s at an angle of 30° with the horizontal, determine the velocity of the bag relative to the belt as it lands on the belt.


Homework Equations


Vi,x = Vi*cos([tex]\theta[/tex])
Vi,y = Vi*sin([tex]\theta[/tex])
(xf-xi) =Vi,x*t
(yf-yi) =Vi,y*t - (1/2)*g*t2
rB = rA+rB/A
vB = vA+vB/A
aB = aA+aB/A

The Attempt at a Solution


I think i've gotten the majority of this problem tackled, so I will list what I have done (as I am highly likely to have done something wrong.) As you can see from the picture below, a linear equation (I think?) is required out of the conveyor belt, so that is the first thing I did.

We know that to make a right triangle with the belt, one side is 90, we're given 20, so the final angle is 70. For pure relations' sake to find a slope, I set the bottom length equal to 10, used tan(20)=opp/10, and found the rise/run to be 3.64/10 which came out to be a slope of .364.

I also set my origin at the location of the duffel bag, which was 1.5 feet above the starting location of the conveyor belt line. So, for my linear equation, I found y=.364x-1.5

Then from there, (I think this is right?) I subbed my xf and yf equations into my linear equation. I was then faced with a quadratic, which, when solved for t, I found t=.3209 s. Fast forwarding a bit more after this I found my final x and y distances.

My x final distance was .6947 ft, while my y final distance was -1.2465 ft.

And...this is where I taper off. I am unsure how to proceed next. I know my final distances, the time it took to hit the conveyor belt...but I am not sure how to relate all of this to find the relative velocity of the bag to the belt.

Could anyone spare some help? I would greatly appreciate it! :smile:

4. F.B.D.
2d14k5c.jpg
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,832
250
Hi Khamul! :smile:
My x final distance was .6947 ft, while my y final distance was -1.2465 ft.

And...this is where I taper off. I am unsure how to proceed next. I know my final distances, the time it took to hit the conveyor belt...but I am not sure how to relate all of this to find the relative velocity of the bag to the belt.
now you need to find the x and y components of the final velocity

to find the relative velocity, you then just subtract the velocity components of the belt :wink:

btw, why did you do all this, instead of simply saying tan20° = 0.364 ? :confused:
We know that to make a right triangle with the belt, one side is 90, we're given 20, so the final angle is 70. For pure relations' sake to find a slope, I set the bottom length equal to 10, used tan(20)=opp/10, and found the rise/run to be 3.64/10 which came out to be a slope of .364.
 
  • #3
24
0
Hi Khamul! :smile:


now you need to find the x and y components of the final velocity

to find the relative velocity, you then just subtract the velocity components of the belt :wink:

btw, why did you do all this, instead of simply saying tan20° = 0.364 ? :confused:
Goood morning tiny-tim, thanks for getting around to helping me so early!:smile:

Huh. Well hey, look at that! I learned something new about slopes, thank you! Also, thank you for steering me in the right direction :smile: I was burned out between this and thermodynamics by midnight last night!
 
  • #4
I am actually working on this problem right now and my question for you is where did you place you axis in this problem?
 

Related Threads on Dynamics - Relative Motion Help?

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
882
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
2
Views
928
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
2
Views
9K
Top