Solving a Ball Roll Down a Slide: Velocity at Bottom

In summary, the problem involves a toddler rolling a ball down a slide with a height of 4m. The ball is a thin spherical shell with a mass of m and a radius of r. To find the velocity of the ball at the bottom of the slide, the conservation of mechanical energy equation can be used, where Iw represents angular momentum and Icm=(2/3)mr^2 is a value that plays a part in the solution.
  • #1
CaptFormal
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0

Homework Statement



A toddler is having fun rolling a ball down a slide of height h=4 m. The ball can be considered as a thin spherical shell, Icm=(2/3)mr^2, with m being its mass and r being its radius. What is the velocity of the ball at the bottom of the slide?

http://schubert.tmcc.edu/enc/51/76a002f3ae50dbbab12d33cf0762512f807c557c31b679999d542c0ad5867fc1faec19c5cc0644a0057420a72734c009d46cf669ed738b61fc0def4a303f9990.gif

Homework Equations



KE(i) + PE(i) + Iw(i) = KE(f) + PE (f) + Iw(f)

KE(i) = Initial Kinetic Energy
PE(i) = Initial Potential Energy
Iw(i) = Initial Inertia*Omega

KE(f) = Final Kinetic Energy
PE(f) = Final Potential Energy
Iw(f) = Final Inertia*Omega

The Attempt at a Solution



I think I am supposed to use the above equation but I am not quite sure. Any suggestions? Thanks.
 
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  • #2
You want to use conservation of mechanical energy, don't you? But Iw is not energy. It is angular momentum.

ehild
 
  • #3
So, what do I do with this value: Icm=(2/3)mr^2? I am sure that it plays a part in solving for the solution.
 

Related to Solving a Ball Roll Down a Slide: Velocity at Bottom

1. What is the formula for calculating velocity at the bottom of a slide?

The formula for calculating velocity at the bottom of a slide is V = √(2gh), where V is the velocity in meters per second (m/s), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the slide in meters (m).

2. How does the angle of the slide affect the velocity at the bottom?

The angle of the slide does not affect the velocity at the bottom, as long as the height of the slide remains the same. The formula for calculating velocity at the bottom only takes into account the height of the slide, not the angle.

3. What factors can affect the velocity at the bottom of a slide?

The main factor that affects the velocity at the bottom of a slide is the height of the slide. Other factors that can impact the velocity include air resistance, friction, and the mass of the object rolling down the slide.

4. Can the velocity at the bottom of a slide be greater than the initial velocity?

No, the velocity at the bottom of a slide cannot be greater than the initial velocity. This is because the object rolling down the slide will experience some form of friction or resistance, which will cause it to lose some of its initial velocity.

5. How can the velocity at the bottom of a slide be measured?

The velocity at the bottom of a slide can be measured using a variety of methods. One common method is to use a stopwatch to measure the time it takes for the object to reach the bottom of the slide, and then use the formula V = d/t (velocity = distance/time) to calculate the velocity. Another method is to use a motion sensor or accelerometer to measure the velocity directly.

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