Solving Box & Ramp Problem at 50° Angle

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In summary, the problem involves a box at the bottom of a frictionless ramp with an initial horizontal velocity of 10 m/s. The box then moves onto the ramp with component velocities of Vx = 5 m/s and Vy = 8.7 m/s. The acceleration in the Y direction is -9.81 m/s^2 and the acceleration in the X direction is 0. The problem asks for the angle of the ramp, the distance traveled in the X and Y directions, and the time it takes to travel those distances. The acceleration due to gravity is constant and independent of the mass of the box. The formula for finding the angle is tan^-1 (Force applied / Force gravity) and the formula for finding
  • #1
mrjeffy321
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Lets say you have a box at the bottom of a frictionless ramp and you give it a velocity (X) of let's say 10 m/s, so that when it gets on the ramp, the components velocities would be:
Vx = 10 * cos (angle)
Vy = 10 * sin (angle)

then once it gets ontp the ramp, the gravitational acceleration changes from
being -9.81 m/s^2 down (Y) to a combination of X and Y acceleration.

I am trying to find the X and Y acceleration, I have been looking at the diagram of the ramp and box and have drawn my force lines to indicate which direction everything has a force exserted on it, but when I goto calculate the acceleration I get very confused.

So let's just say in this example the ramp is at an angle of 50 degrees, the box has in initial X velocity (before the ramp) of 10 m/s and we will esimate gravitational acceleration at -10 m/s^2.
so we now have the box on the ramp with:
Vx = 10 * cos (60) = 5 m/s
Vy = 10 * sin (60) = 8.7 m/s

acceleration X = ? -10 * sin (60) = -8.7 m/s^2 ?
acceleration Y = ? -10 * cos (60) = -5 m/s^2 ?

is that right? or is it:

acceleration Y = ? -10 * sin (60) = -8.7 m/s^2 ?
acceleration X = ? -10 * cos (60) = -5 m/s^2 ?
 
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  • #2
Define your coordinate system as X is parrallel to the ramp and Y is parrallel to the normal force.


Then: F=ma and F due to grav is mg.
I think you might be confused because your box is massless. You have to sum your forces, don't try adding accelerations.
 
  • #3
OK, I get that now,

so to find the acceleration in a particular direction use the opposite (sin/cos) finction that you used to find its velocity in that difrection.
so it would be:
acceleration X = ? -10 * sin (60) = -8.7 m/s^2 ?
acceleration Y = ? -10 * cos (60) = -5 m/s^2 ?

this is what I was afraid of, that just caused more problem than it solved, because in the long run of this problem, I am trying to find the angle of the ramp, and the distance traveled in each direction (X and Y).
 
  • #4
I don't think this can be done without a mass of the box.

Do you have the actual text of the problem?
 
  • #5
No, the mass of the box is not needed in the problem, I am pretty sure of that (it isn't give anyway). I do have the actual text of the problem, an I can give it to you if you want, but I was trying to maintain a certain degree of integrity with this by doing it myself.

I will tell you what it wants:
basicaly, the problem gives you a box at a ramp with an initial horizontal velocity (which you then convert to its componet velocity), and it gives you a distance traveled (X). it then asks you to find the angle of the ramp and the distance traveled (Y) and the time it takes.

I assume that I can use the formula: Vf = Vi + a * t, to find the time, and thus the distance traved along with this formula, d = (Vi * t) + (1/2*a*t^2).
but then I ran across this other way of finding the angle:
angle = tan^-1 (Force applied / Force gravity)
and you can get the force applied by using the formula:
Vf^2 = Vi^2 + 2 * a * d
 
  • #6
But the magnitude of the acceleration due to gravity is directly related to the mass...

Well then, I am confused. Oh well!
 
  • #7
o great, now I have spreak my confusion to the only other person who was helping me.

the magnitude of acceleration is related to the angle of the slope. the magnitude of the force is realated to the mass. but in this problem, I don't care about force.



Here is what I got for an answer, but I am almost certain that it is wrong.
Dx = 5.1 m
Dy = 8.6 m
angle = 59 degrees
time = 1 second up, 1 second down

I say that it is almost certainly wrong because I got that back when I still wasnt sure how to correctly calculate the component accelerations, and I thing I did it wrong.
 
  • #8
Gmaximus said:
But the magnitude of the acceleration due to gravity is directly related to the mass...

Well then, I am confused. Oh well!

Yes, you are very confused. The acceleration due to gravity on an object is independent of the object's mass!

(The force is proportional to the object's mass but then F= ma.)
 
  • #9
[QU0TE= mrjeffy321]"then once it gets ontp the ramp, the gravitational acceleration changes from
being -9.81 m/s^2 down (Y) to a combination of X and Y acceleration."

No. Since you have changed the velocity (up the slope) to
Vx = 10 * cos (60) = 5 m/s
Vy = 10 * sin (60) = 8.7 m/s (the "speed" up the ramp is 10 m/s)
it is clear that x and y here are horizontal and vertical. The acceleration is still
Ax= 0, Ay= -9.81.
 
  • #10
HallsofIvy said:
Yes, you are very confused. The acceleration due to gravity on an object is independent of the object's mass!

(The force is proportional to the object's mass but then F= ma.)


Oh, Duh. I shouldn't try to help people so late at night.

Obviously, g is constant for everything. Funny how stupid i can be.

Sorry Mr.Jeffy, I sincerely apologize for confounding you further.
 
  • #11
so I shouldn't be trying to change the acceleration into X and Y acceleration, i should leave it as all Y.
 

What is the purpose of solving the Box & Ramp Problem at 50° angle?

The purpose of solving the Box & Ramp Problem at 50° angle is to understand the relationship between force, mass, and acceleration when an object is placed on an inclined plane. This problem helps to demonstrate the principles of Newton's laws of motion.

What are the variables involved in solving the Box & Ramp Problem at 50° angle?

The variables involved in solving this problem include the angle of inclination (50°), the mass of the object, the coefficient of friction between the object and the ramp, and the force acting on the object. These variables are used to calculate the acceleration and determine the motion of the object on the ramp.

How does the angle of inclination affect the motion of the object in the Box & Ramp Problem?

The angle of inclination plays a significant role in determining the motion of the object on the ramp. A steeper angle will result in a greater force of gravity pulling the object down the ramp, leading to a faster acceleration. A lower angle will result in a weaker force of gravity, leading to a slower acceleration.

What is the formula used to solve the Box & Ramp Problem at 50° angle?

The formula used to solve this problem is F=ma, where F is the force acting on the object, m is the mass of the object, and a is the acceleration. This formula can be modified to include the angle of inclination and the coefficient of friction, depending on the specific details of the problem.

How can the Box & Ramp Problem at 50° angle be applied in real-life situations?

The principles and concepts learned from solving the Box & Ramp Problem at 50° angle can be applied in various real-life situations. For example, understanding the relationship between force, mass, and acceleration can be useful in designing ramps or inclined planes for moving heavy objects. It can also be applied in the study of motion and mechanics, such as in the field of engineering or physics.

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