Solving Ball Roll Down Ramp: 200 m/s Speed for Steel Ball

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In summary, the smaller ball would have a velocity of 324.7 cm/s when it impacts the steel ball, which is the same as the final velocity of the steel ball.
  • #1
ixbethxi
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A 110 g marble rolls down a 39.0 deg. incline. At the bottom, just after it exits onto a horizontal table, it collides with a 290 g steel ball at rest.

How high above the table should the marble be released to give the steel ball a speed of 200 m/s?

well first i tried to use the formula for perfectly elastic collisions
(Vf)steel= (2m(marble)/ m(marble)+m(steel))*v_f(ball1)

and i solved for v_f and then i plugged that into mgh(initial)= 0.5m*v^2

and none that didnt work so now I am confused again
 
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  • #2
I just want to be sure. Do you mean final velocity of 20 m/s? Or do you really mean 200 m/s?

In an elastic collision you can assume that the Kinetic Energy of the balls will be the same before and after.

KE = 1/2 mv^2

1) Find the final KE of the steel ball after impact (v=20 or v=200).
2) Use this number to calculate the velocity of the smaller ball just prior to impact.
3) Calculate the initial height necessary in order to accelerate the ball to the velocity found in step 2.

Furthermore if I'm not mistaken, use the sin(39) to help calculate the acceleration of the ball down the ramp. After all if the ball were on a table, the angle would be zero and sin(0) = 0. If the ball were up against a wall the angle would be 90 (straight down), and sin (90) = 1.
 
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  • #3
o whoops.. i meant cm/s
 
  • #4
ok this is what i got so far

0.5*m*v^2= 0.5*.290kg*200cm/s^2= 5800

5800= (0.5)(.110kg)(v^2)
i solved for v and i got 324.7cm/s^2

now i know this is the velocity at the bottom of the ramp but i don't know hwo to get the height from here.
 
  • #5
Use conservation of energy.

gain in KE = loss in PE.
 
  • #6
what is the unit of energy you got?
 

FAQ: Solving Ball Roll Down Ramp: 200 m/s Speed for Steel Ball

What is the purpose of solving for the speed of a steel ball on a ramp?

The purpose of solving for the speed of a steel ball on a ramp is to understand the principles of motion and energy conservation. By determining the speed of the ball, we can also calculate its kinetic energy and potential energy at different points along the ramp.

What factors affect the speed of a steel ball on a ramp?

The speed of a steel ball on a ramp is affected by several factors such as the angle of the ramp, the surface of the ramp, the mass of the ball, and the presence of any external forces such as friction or air resistance. These factors all contribute to the acceleration of the ball down the ramp.

How is the speed of a steel ball on a ramp calculated?

The speed of a steel ball on a ramp can be calculated using the equation v = √(2gh), where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the ramp. This equation assumes no external forces acting on the ball and neglects any friction or air resistance.

Can the speed of a steel ball on a ramp reach 200 m/s?

It is highly unlikely for the speed of a steel ball on a ramp to reach 200 m/s. This speed is extremely high and would require a very steep ramp and a perfectly smooth and frictionless surface. In most cases, the ball will reach a maximum speed of around 10-20 m/s.

How can the speed of a steel ball on a ramp be measured?

The speed of a steel ball on a ramp can be measured using a stopwatch and measuring the time it takes for the ball to travel a certain distance. This distance can be marked on the ramp or measured using a ruler or measuring tape. The speed can then be calculated using the equation v = d/t, where v is the speed, d is the distance, and t is the time.

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