Ball Rolling Off of Table

In summary, The ball reaches the end of the table in 0.178584 seconds, covering a horizontal distance of 14.016 cm. The table is 86.49 cm tall. To determine the ball's velocity and how far it will roll, you need to convert the distance to meters and use the equations y=vit+.5(g)(t)^2 and x=vt. You also need to multiply the falling time by the horizontal velocity to get the distance from the table. The question is unclear about the velocity and distance, so further clarification is needed.
  • #1
Londoncalling
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0
1. The Lab
The ball reaches the end of the table in .178584 s, a distance of 14.016 cm. The table is 86.49 cm tall. What is the ball's velocity and far will it roll?

Homework Equations


y=vit+.5(g)(t)2
x=vt

The Attempt at a Solution


I assumed vi was 0 and got that time=4.201, but that didn't seem to make sense. Should I convert the 86.49 into .8649 m? Because then I get that time=.4 ish and that can't be right...
Edit: Do I multiply the time (4.20) by vhorizontal? 4.20*(14.016/.1785)=32.98428?
 
Last edited:
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  • #2
The question is rather unclear. Is the velocity when the ball reaches the ground meant, or when it leaves the table?. Does "and far will it roll?" mean how far from the table will it land?
You certainly need to convert the distance to meters to get the falling time. Why is .4ish not right for the time? You do need to multiply the falling time with the horzontal speed to get the distance from the table. Watch the units.

To answer the velocity question you need to include both horizontal and vertical speed.
 
  • #3


I would approach this problem by first clarifying the variables and units being used. It appears that the given information is in units of seconds and centimeters, so I would convert the height of the table to meters (0.8649 m) to be consistent. Then, using the equations for motion, I would calculate the initial velocity of the ball by rearranging the equation for horizontal motion, x=vt, to solve for v. This gives a velocity of 78.6 cm/s.

Next, I would use the equation for vertical motion, y=vit+0.5gt^2, to solve for t, the time it takes for the ball to reach the end of the table. Plugging in the known values, including the initial velocity of 78.6 cm/s and the distance of 14.016 cm, I get a time of 0.178 s. This is consistent with the given information, so it appears to be a reasonable solution.

Finally, I would use the equation x=vt to calculate the horizontal distance the ball will roll off the table, using the calculated velocity of 78.6 cm/s and the time of 0.178 s. This gives a distance of 13.996 cm, which is very close to the given distance of 14.016 cm.

In conclusion, the ball's velocity is 78.6 cm/s and it will roll a distance of 13.996 cm off the table. It is important to be consistent with units and use the appropriate equations for motion in order to accurately solve this problem.
 

1. What causes a ball to roll off of a table?

The main reason a ball rolls off of a table is due to the force of gravity. When the ball is placed on the edge of the table, it is not stable and is pulled towards the ground by the Earth's gravitational pull.

2. What is the role of friction in a ball rolling off of a table?

Friction plays a significant role in a ball rolling off of a table. As the ball moves, it experiences friction with the table's surface, which slows it down and eventually stops its motion. When the ball is placed near the edge of the table, there is less surface area in contact with the table, resulting in less friction and allowing the ball to roll off more easily.

3. How does the shape of the ball affect its motion off of a table?

The shape of the ball can impact its motion off of a table. A spherical ball will have a more predictable and consistent path compared to an irregularly shaped ball. A spherical ball also has a lower center of mass, making it more stable and less likely to roll off the table.

4. Can the height of the table affect how far the ball rolls off?

Yes, the height of the table can affect how far the ball rolls off. The higher the table, the longer the ball has to accelerate due to gravity, resulting in a longer distance traveled. Additionally, the height can affect the ball's speed and angle at which it leaves the table, ultimately impacting its distance traveled.

5. Are there ways to prevent a ball from rolling off of a table?

Yes, there are various ways to prevent a ball from rolling off of a table. Placing a barrier or edge guard around the table can provide a physical barrier to stop the ball. Additionally, placing the ball further away from the edge of the table or using a ball with a lower center of mass can also prevent it from rolling off.

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