Physics Energy - how fast ball is moving from certain height

In summary, to find the speed of a ball rolling down a ramp from a given height, you can use the conservation of energy principle and the equation mgh = (1/2)mv^2 + (1/2)I(ω^2), where I is the moment of inertia of the ball and ω is the angular speed (which can be calculated using v/r for pure rolling). This takes into account both the translational kinetic energy and the rotational kinetic energy of the ball.
  • #36
nasu said:
It may be a rounding error.
Or it may be a little more complicated. Depends on the level of your class.

Have you learned about moment of inertia and rotational kinetic energy?
They say that the ball is rolling so you may be supposed to consider the rotation of the ball too.
In this case the kinetic energy will have two terms,
KE=1/2mv^2 + 1/2 I ω^2
where I is the moment of inertia of the ball and ω is the angular speed. For rolling without slipping, ω is v/R where R is the radius of the ball.
Have you seen any of these?

The question specifically mentions that the ball rolls. That means:

change in gravitational potential energy = (translation kinetic energy)+(rotational kinetic energy)

assuming ball is a solid sphere, you should know the moment of inertia of sphere. and as nasu already mentioned for pure rolling [itex] ω= \frac{v}{r}[/itex]
[itex]mgh = \frac{1}{2}mv^2 + \frac{1}{2}Iω^2[/itex]
[itex]mgh = \frac{1}{2}mv^2 + \frac{1}{2}\frac{2mr^2}{5}ω^2[/itex]
[itex]mgh = \frac{1}{2}mv^2 + \frac{1}{2}\frac{2mr^2}{5}(\frac{v}{r})^2[/itex]

the final equation would come out to be [itex]mgh = \frac{7}{10}mv^2[/itex]
 
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<h2>1. What is the formula for calculating the speed of a ball from a certain height?</h2><p>The formula for calculating the speed of a ball from a certain height 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 in meters (m).</p><h2>2. Does the mass of the ball affect its speed when dropped from a certain height?</h2><p>Yes, the mass of the ball does affect its speed when dropped from a certain height. According to the formula v = √2gh, the speed is directly proportional to the square root of the height. This means that a heavier ball will have a greater speed when dropped from the same height compared to a lighter ball.</p><h2>3. How does air resistance affect the speed of a ball when dropped from a certain height?</h2><p>Air resistance, also known as drag, can slow down the speed of a ball when dropped from a certain height. This is because the force of air resistance acts in the opposite direction of motion, thus reducing the acceleration of the ball. However, the effect of air resistance is more significant for objects with a larger surface area, such as a parachute, compared to a small ball.</p><h2>4. Can the speed of a ball be greater than its initial potential energy when dropped from a certain height?</h2><p>No, the speed of a ball cannot be greater than its initial potential energy when dropped from a certain height. This is because the total energy of a system, including both kinetic and potential energy, remains constant. Therefore, as the ball falls and gains kinetic energy, its potential energy decreases, and the total energy remains the same.</p><h2>5. How does the height from which a ball is dropped affect its speed?</h2><p>The height from which a ball is dropped directly affects its speed. According to the formula v = √2gh, the speed is directly proportional to the square root of the height. This means that the higher the ball is dropped from, the greater its speed will be when it reaches the ground. Additionally, the height also affects the potential energy of the ball, with a higher drop height resulting in a greater potential energy.</p>

Related to Physics Energy - how fast ball is moving from certain height

1. What is the formula for calculating the speed of a ball from a certain height?

The formula for calculating the speed of a ball from a certain height 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 in meters (m).

2. Does the mass of the ball affect its speed when dropped from a certain height?

Yes, the mass of the ball does affect its speed when dropped from a certain height. According to the formula v = √2gh, the speed is directly proportional to the square root of the height. This means that a heavier ball will have a greater speed when dropped from the same height compared to a lighter ball.

3. How does air resistance affect the speed of a ball when dropped from a certain height?

Air resistance, also known as drag, can slow down the speed of a ball when dropped from a certain height. This is because the force of air resistance acts in the opposite direction of motion, thus reducing the acceleration of the ball. However, the effect of air resistance is more significant for objects with a larger surface area, such as a parachute, compared to a small ball.

4. Can the speed of a ball be greater than its initial potential energy when dropped from a certain height?

No, the speed of a ball cannot be greater than its initial potential energy when dropped from a certain height. This is because the total energy of a system, including both kinetic and potential energy, remains constant. Therefore, as the ball falls and gains kinetic energy, its potential energy decreases, and the total energy remains the same.

5. How does the height from which a ball is dropped affect its speed?

The height from which a ball is dropped directly affects its speed. According to the formula v = √2gh, the speed is directly proportional to the square root of the height. This means that the higher the ball is dropped from, the greater its speed will be when it reaches the ground. Additionally, the height also affects the potential energy of the ball, with a higher drop height resulting in a greater potential energy.

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