Calculating Kinetic Energy and Speed of a Rolling Sphere on an Inclined Surface

  • Thread starter Clutch306
  • Start date
In summary, a solid sphere of radius 0.100m and mass 14.3kg rolls up a 30 degree incline without slipping. At an initial position, the sphere's total kinetic energy is 90.1J. (a) The rotational energy of the sphere is being asked for. (b) The speed of the center of mass at the initial position is unknown. After moving 1.00m up the incline from its initial position, (c) the sphere's total kinetic energy is unknown. (d) The speed of its center of mass is also unknown.
  • #1
Clutch306
7
0
A solid sphere of radius 0.100m and mass 14.3kg rolls without slipping up a surface inclined at 30 degrees to the horizontal. At a certain initial position the sphere's total kinetic energy is 90.1J.
(a) How much of this initial kinetic energy is rational?
(b) What is the speed of the center of mass of the sphere at the initial position?
After the sphere has moved 1.00m up along the incline from its initial position:
(c) What is its total kinetic energy?
(d) What is the speed of its center of mass?
 
Physics news on Phys.org
  • #2
"rational?" rotational is what I think you meant to write. Well, it would be nice to have some energy to converse with. I do believe I have some energy to help you anyway.

Well, what's the first item you do not understand how to compute, for example, the moment of inertia of the sphere? aah got to go
 
  • #3


(a) To calculate the rational kinetic energy, we need to first determine the potential energy of the sphere at the initial position. The potential energy is given by the formula PE = mgh, where m is the mass of the sphere, g is the acceleration due to gravity, and h is the height of the sphere above the ground. Since the sphere is at a 30 degree incline, the height can be calculated using trigonometry as h = 0.100m * sin(30) = 0.050m. Plugging in the values, we get PE = (14.3kg)(9.8m/s^2)(0.050m) = 7.01J. Therefore, the rational kinetic energy is 90.1J - 7.01J = 83.09J.

(b) To find the speed of the center of mass at the initial position, we can use the formula for kinetic energy KE = 1/2mv^2, where m is the mass of the sphere and v is the speed of the center of mass. Plugging in the values, we get 90.1J = (1/2)(14.3kg)v^2. Solving for v, we get v = √(2*90.1J/14.3kg) = 2.98m/s. Therefore, the speed of the center of mass at the initial position is 2.98m/s.

(c) To find the total kinetic energy after the sphere has moved 1.00m up the incline, we can use the formula for potential energy PE = mgh, where m is the mass of the sphere, g is the acceleration due to gravity, and h is the height of the sphere above the ground. Since the sphere has moved 1.00m up the incline, the height is now h = 0.100m * sin(30) + 1.00m = 1.05m. Plugging in the values, we get PE = (14.3kg)(9.8m/s^2)(1.05m) = 138.99J. Therefore, the total kinetic energy is 138.99J.

(d) To find the speed of the center of mass after the sphere has moved 1.00m up the incline, we can use the formula for kinetic energy KE = 1/
 

What is the meaning of "I need some help quick"?

"I need some help quick" is a common phrase used when someone is in urgent need of assistance or support. It conveys a sense of urgency and a request for immediate help.

Why do people use the phrase "I need some help quick"?

People use this phrase when they are facing a problem or a difficult situation and they need someone to assist them quickly. It can also be used when someone is overwhelmed and needs extra help to complete a task or project.

What is the best way to respond to someone who says "I need some help quick"?

The best way to respond to this phrase is by offering your assistance and asking the person what kind of help they need. It is important to act quickly and efficiently to address their urgent need.

How can I provide help quickly to someone who says "I need some help quick"?

One way to provide help quickly is by actively listening to the person's needs and offering solutions or resources that can assist them. It is also important to act promptly and efficiently to provide the necessary support.

What are some common situations where someone might say "I need some help quick"?

People may use this phrase in a variety of situations, such as when they are in a time-sensitive or stressful situation, when they are facing a difficult task, or when they are experiencing an emergency. It can also be used when someone needs assistance with a complex problem or situation.

Similar threads

  • Introductory Physics Homework Help
Replies
21
Views
1K
Replies
10
Views
309
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
19
Views
3K
Replies
1
Views
487
  • Introductory Physics Homework Help
Replies
6
Views
608
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
29
Views
822
  • Introductory Physics Homework Help
Replies
32
Views
2K
Replies
24
Views
1K
Back
Top