Kinetic Energy of a Bowling Ball

• PeachBanana
In summary, the conversation involves a bowling ball of mass 7.2 kg and radius 9.1 cm rolling down a lane at 3.0 m/s. The question is asking for the total kinetic energy of the bowling ball, which is calculated by adding the rotational and translational kinetic energies. The formula for rotational kinetic energy is KE rot. = 1/2 Iω^2, where I is the moment of inertia and ω is the angular velocity. By using the formula for a uniform sphere, the moment of inertia is calculated to be 0.0238492 kg * m^2. The angular velocity is found to be 0.3296 rad./s. Adding in the translational kinetic energy
PeachBanana

Homework Statement

A bowling ball of mass 7.2 kg and radius 9.1 cm rolls without slipping down a lane at 3.0 m/s.

What is the total kinetic energy of the bowling ball?

Homework Equations

KE rot. = 1/2 Iω^2

The Attempt at a Solution

KE initial = 0 J (I'm assuming it started from rest).
I = 2/5 (7.2 kg)(0.091 m)^2
I = 0.0238492 kg * m^2
I used the formula for a uniform sphere to calculate this.

3.0 m/s / 0.091 m = 0.3296 rad./s

KE final = 1/2 (0.0238492 kg*m^2)(0.3296 rad./s)^2
KE final = 1.3 * 10 ^ -3 J

I'm thinking I messed up at the "I" variable because my answer is tiny.

Last edited:
PeachBanana said:
3.0 m/s / 0.091 m = 0.3296 rad./s
Recheck this calculation.

Also: Don't forget the translational KE.

DocAl - I redid the calculation and read the exponent of 3.296 as -1 and not +1. I added in the translational kinetic energy and got the right answer of 45 J.

Good!

Your calculation for the moment of inertia (I) looks correct. However, the value for ω (angular velocity) should be in units of radians per second (rad/s), not just radians. So your calculation for the final kinetic energy should be:

KE final = 1/2 (0.0238492 kg*m^2)(0.3296 rad/s)^2 = 0.001954 J

This is still a relatively small value, but it makes sense because the bowling ball is not moving very fast. If you compare this to the kinetic energy of a car traveling at 60 mph (26.8 m/s), which would have a mass of around 1000 kg, the kinetic energy would be approximately 360,000 J. So even though the bowling ball has a smaller mass, its slower speed results in a much smaller kinetic energy.

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is a type of mechanical energy and is directly related to the mass and velocity of the object.

How is kinetic energy calculated?

The formula for calculating kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity. In simpler terms, the kinetic energy of an object is equal to half of its mass multiplied by the square of its velocity.

What is the relationship between kinetic energy and bowling balls?

Bowling balls have kinetic energy because they are in motion when they are thrown down the bowling lane. The heavier the ball and the faster it is thrown, the more kinetic energy it will have.

What happens to the kinetic energy of a bowling ball when it hits the pins?

When a bowling ball hits the pins, its kinetic energy is transferred to the pins, causing them to move and potentially knock down other pins. Some of the kinetic energy may also be converted into other forms of energy, such as sound and heat.

Can the kinetic energy of a bowling ball be changed?

Yes, the kinetic energy of a bowling ball can be changed by altering its mass or velocity. For example, using a heavier or lighter ball, or throwing the ball faster or slower, will result in a different amount of kinetic energy. Additionally, friction and air resistance can also affect the kinetic energy of a bowling ball.

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