Ball on ramp and Merry Go Round problem

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In summary: You should get two answers, one of which is right and one of which is wrong. Which one is the right one?In summary, two conversations are summarized. The first one discusses a ball rolling down a ramp with a 23 degree angle, its initial velocity and acceleration, and how long it takes to reach the bottom of the ramp. It also talks about the ball's trajectory when it reaches the bottom of the ramp and goes up the ramp on the right. The second conversation discusses a person standing on a Merry-Go-Round, tossing a ball in the air, and the components of the ball's velocity when it hits the ground. Both conversations involve calculations and equations to solve for different variables.
  • #1
john8910
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1) A small ball rolls down the frictionless ramp on the left (shown below). The angle of the
ramp is approximately 23 degrees, as shown, so the acceleration of an object rolling
down the ramp is g sin(23 deg) = 4 m/s^2.

The ball is given a push when it starts 1 meter away from the bottom of the ramp, so
initially it’s rolling downward with a velocity of 1 m/s.

Once the ball reaches the bottom of the ramp on the left, it starts rolling up the ramp on the right.

a) How much time does it take to reach the bottom of the ramp on the left?
(b) How fast is it going when it reaches the bottom of the ramp on the left?
(c) How far up the second ramp does the ball roll?
(d) How much time does it take to travel from the bottom of the ramp to the top of the
ramp on the right?


knowns:
Θ = 23, a = 4 m/s^2, xi= 0m, xf = 1m, vi = 1 m/s

i wasnt sure how to get a, so i started on b first, then i got a, but i don't know if this is the correct way to do it.
b)i used Vf^2 = Vi^2 + 2ax, and i got 9 m/s for final velocity
a) d = ((vi+vf)/2)*t, and i got 0.5s
c) I am sure on this one but i think i use vf^2 = Vi^2 + 2ax, and i got approx. 10 m
d) df = di+vit + 1/2at^2

practically, I am not sure how to start on a, and i need help on c and d.






2) I’m standing on the edge of a Merry-Go-Round that’s rotating around. I’m holding a ball in my hand. I toss it straight up in the air (in my reference frame).

When I toss the ball up in the air, the vertical component of the ball’s velocity is 5 meters per second. I’m 3 meters away from the center of the Merry-Go-Round, and it takes 6 seconds for the Merry-Go-Round to travel in a circle. It’s traveling clockwise.

(a) If the ball is 1 meter above the ground when tossed upward, how much time does the ball spend in the air before hitting the ground?
(b) How far away from my starting point does the ball land?
(c) What are all of the components of the ball’s velocity when it hits the ground?
Assume that the direction out of the page is the z direction

vi = 5m/s, r = 3 m ..

a) I am guessing y0= 0m, y1= 1m, vi = 5m/s, vf = 0m/s, a = -9.8 m/s2
i have trouble when the initial vi is not 0, i know i have to use xf=xi+vit+1/2at2
but I am not sure how to get t by itself.
b and c I am lost...
 

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  • #2
john8910 said:
1)...

i wasnt sure how to get a, so i started on b first, then i got a, but i don't know if this is the correct way to do it.
b)i used Vf^2 = Vi^2 + 2ax, and i got 9 m/s for final velocity
a) d = ((vi+vf)/2)*t, and i got 0.5s
c) I am sure on this one but i think i use vf^2 = Vi^2 + 2ax, and i got approx. 10 m
d) df = di+vit + 1/2at^2

practically, I am not sure how to start on a, and i need help on c and d.
To solve a first, you can use the same formula that you have listed for d. (But it's perfectly OK to solve then in any order--there are several ways to attack this problem.)

Redo your calculation for b; looks like you forgot to take the square root.

Also, use a more accurate calculation for the acceleration. (Only round off at the end.)
2)...

a) I am guessing y0= 0m, y1= 1m, vi = 5m/s, vf = 0m/s, a = -9.8 m/s2
i have trouble when the initial vi is not 0, i know i have to use xf=xi+vit+1/2at2
but I am not sure how to get t by itself.
b and c I am lost...
That formula will give you a quadratic equation, which you can solve. xi = 1; xf = 0.
 
  • #3






First, let's address the problem of the ball rolling down a ramp and then up another ramp. The acceleration of the ball is given by g sin(23 deg) = 4 m/s^2, which means that its velocity will increase by 4 m/s every second. To determine the time it takes for the ball to reach the bottom of the ramp on the left, we can use the equation d = vi*t + 1/2*a*t^2, where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time. In this case, d = 1m, vi = 1 m/s, and a = 4 m/s^2. Solving for t, we get t = 0.5 seconds. This means that it takes 0.5 seconds for the ball to reach the bottom of the ramp on the left.

To determine the final velocity of the ball when it reaches the bottom of the ramp on the left, we can use the equation vf^2 = vi^2 + 2*a*d. In this case, vf is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance traveled. Plugging in the values, we get vf = 9 m/s. This is the final velocity of the ball when it reaches the bottom of the ramp on the left.

Now, to determine how far up the second ramp the ball will roll, we can use the equation vf^2 = vi^2 + 2*a*d, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance traveled. In this case, vf = 9 m/s, vi = 0 m/s (since the ball starts from rest at the bottom of the ramp on the left), and a = -4 m/s^2 (since the ball is now rolling up the ramp in the opposite direction). Solving for d, we get d = 10 m. This means that the ball will roll up the second ramp for a distance of 10 meters.

To determine the time it takes for the ball to travel from the bottom of the ramp to the top of the ramp on the right, we can use the equation vf = vi + a*t, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the
 

1. What is the "Ball on ramp and Merry Go Round problem"?

The "Ball on ramp and Merry Go Round problem" is a popular physics problem that involves a ball rolling down a ramp and onto a rotating merry-go-round. The problem requires the use of concepts such as centripetal force, rotational motion, and conservation of energy to solve.

2. What are the key factors to consider when solving the "Ball on ramp and Merry Go Round problem"?

The key factors to consider when solving the "Ball on ramp and Merry Go Round problem" include the mass and velocity of the ball, the radius and angular velocity of the merry-go-round, and the angle and height of the ramp. These factors affect the forces acting on the ball and the energy involved in the system.

3. How do I approach solving the "Ball on ramp and Merry Go Round problem"?

To solve the "Ball on ramp and Merry Go Round problem", you should first draw a free-body diagram of the ball and identify all the forces acting on it. Then, you can use equations of motion and energy conservation to determine the final velocity and position of the ball on the merry-go-round.

4. What are the common mistakes made when solving the "Ball on ramp and Merry Go Round problem"?

One common mistake is forgetting to account for the rotational motion of the merry-go-round and only considering the linear motion of the ball. Another mistake is not considering conservation of energy and assuming that all of the initial potential energy of the ball is converted into kinetic energy.

5. How can I apply the concepts from the "Ball on ramp and Merry Go Round problem" to real-life situations?

The "Ball on ramp and Merry Go Round problem" can help you understand and apply the concept of centripetal force, which is important in many real-life situations such as the motion of satellites, amusement park rides, and car accidents. It also demonstrates the principles of conservation of energy and angular momentum, which are crucial in many scientific fields.

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