Ball rolling down an incline: How to calculate final velocity?

In summary: I) = .5v^2 (1 + (1/I)) = v^2In summary, the ball of mass 2.80 kg and radius 0.153 m, released from rest on a plane inclined at an angle θ = 41.0° with respect to the horizontal, has a moment of inertia of 7.186 kg * m^2. By applying the conservation of energy and solving for the translational kinetic energy and rotational kinetic energy, the speed of the ball after rolling a distance of 1.60 m is equal to the square root of the potential energy divided by 0.5 multiplied by the sum of
  • #1
jti3066
46
0

Homework Statement



A ball of mass 2.80 kg and radius 0.153 m is released from rest on a plane inclined at an angle θ = 41.0° with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.60 m? Assume that the ball rolls without slipping, and that its moment of inertia about its center of mass is 1.80E-2 kg·m2.


Homework Equations



I = Icm + M(d^2)...parallel-axis theorem

wf ^2 = wi^2 + 2a(thetaF - thetaI)...constant angular acceleration

theta = S/r

v=wr

The Attempt at a Solution



I think I need to use the parallel-axis theorem to solve for one step in the problem, so...

I = 0.0180 + 2.8(1.6^2) = 7.186 kg * m^2

Next I found how many "radians" the ball travels in 1.6 m...

C = 2"pi"r = 2"pi" * .153m = .936 m (circumference of ball)

1rad = .936 m

1.6m * (1rad/.936m) = 1.7 radians

I am not even sure how to solve this problem...I did the above equations so I could see if I was going on the right track by a process of elimination...usually I don't worry about the actual numbers until the end of the problem...i.e. if I just use the units in the equations and my "answer" is in the correct units it usually means I am on the correct path...Please help me solve this problem...
 
Physics news on Phys.org
  • #2
Apply the conservation of energy.
The potential energy = Translational kinetic energy + rotational kinetic energy.
Angle is given, displacement along the inclined plane is given. From that find height through which the ball rolls.
 
  • #3
Ok...thanks

mg(d*sin(theta)= .5m *v^2 + .5I(v/r)^2
 

1. How does the angle of the incline affect the speed of the ball?

The angle of the incline has a direct impact on the speed of the ball. The steeper the incline, the faster the ball will roll. This is due to the force of gravity acting on the ball and causing it to accelerate down the incline.

2. What factors affect the overall distance the ball will roll down the incline?

The distance the ball will roll down the incline is affected by several factors, including the angle of the incline, the initial height of the ball, and any friction or resistance present on the surface of the incline.

3. Does the mass of the ball make a difference in its speed down the incline?

Yes, the mass of the ball does have an impact on its speed down the incline. The greater the mass of the ball, the more force of gravity is needed to accelerate it down the incline, resulting in a slower speed.

4. How does the surface of the incline affect the ball's motion?

The surface of the incline can have an impact on the ball's motion. A smoother surface will result in less friction and a faster speed, while a rougher surface will create more friction and slow the ball down.

5. Can the ball's shape affect how it rolls down the incline?

Yes, the shape of the ball can impact its motion down the incline. A round ball will have a more even distribution of weight, leading to a smoother roll, while a ball with an uneven shape may have an irregular motion down the incline.

Similar threads

Replies
10
Views
313
  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
14
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
4K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
17
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Back
Top