Solving Ball Hitting Ramp Physics Problem

  • Thread starter DrKn
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    Ball Ramp
In summary, the problem involved finding the angle between a ramp and the horizontal, as well as the angle between the ramp and an initial velocity. The coordinate system was repositioned and equations were modeled, but when solving for theta using the Pythagorean theorem, a pure number was not obtained. Further assistance is needed.
  • #1
DrKn
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http://img384.imageshack.us/img384/5267/physicsproblem3aq.jpg

This is my problem.


I called the angle between ramp and horizontal theta.

Then, i formed a rectangle between V0 and the ramp, and found the angle between the ramp and V0 is also theta.


Then, i repositioned my coordinate system, so that the x-axis is parallel to the ramp's hypotenuse.


Then, i modeled:
(delta) x = V0cos(theta)* t + 1/2 g sin(theta) * t^2
(delta) y = V0sin(theta) * t + 1/2 g cos(theta) * t^2

and i plugged it into the pythagorean theorem.

when i solved for theta, i don't get a pure number, so i know its wrong.

need major help :cry:
 
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  • #2
How did you "plut it into the pythagorean theorem"? What right triangle did you use? What is the hypotenuse, legs?
 
  • #3
the triangle legs was delta x and delta y, and the range was the hypotenuse
 

1. How do I calculate the velocity of a ball rolling down a ramp?

The velocity of a ball rolling down a ramp can be calculated using the formula v = √(2gh), where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the ramp.

2. How does the angle of the ramp affect the distance the ball travels?

The angle of the ramp affects the distance the ball travels because it determines the initial velocity of the ball. A steeper ramp will result in a higher initial velocity, causing the ball to travel a longer distance. However, the angle also affects the amount of friction and air resistance acting on the ball, which can impact the distance traveled as well.

3. What is the relationship between the mass of the ball and its acceleration down the ramp?

The mass of the ball does not affect its acceleration down the ramp. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the force applied to it, and inversely proportional to its mass. As the ball rolls down the ramp, the force of gravity acting on it remains constant, so its mass does not affect its acceleration.

4. How does the surface of the ramp affect the motion of the ball?

The surface of the ramp can affect the motion of the ball in several ways. A rough surface will cause more friction, slowing down the ball's motion. A smooth surface will result in less friction, allowing the ball to travel further. Additionally, a ramp with grooves or bumps may cause the ball to bounce or change direction, impacting its motion as well.

5. How can I determine the final velocity of the ball at the bottom of the ramp?

To determine the final velocity of the ball at the bottom of the ramp, you can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (in this case, due to gravity), and t is the time it takes for the ball to reach the bottom of the ramp. You can also use the formula v² = u² + 2as, where s is the distance traveled down the ramp.

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