Rolling ball down slope at specific time

In summary, to find the equation for the velocity of a solid ball rolling down a slope with a diameter of 0.5m and a mass of 0.1kg, you can use the energy equations and the moment of inertia of the sphere. By substituting these values, you can solve for the time (t) variable in the equation.
  • #1
havetolovemus
1
0

Homework Statement


A uniform solid ball rolls down a slope. If the ball has a diameter of .5m and a mass of .1 kg find the following:

The equation which describes the velocity of the ball at any time, given that it starts from rest.


Homework Equations



I've tried using energy equations, thus: 1/2 Iw^2+1/2Mv^2+mgh = constant (Kf +Uf = Ki + Ui) but that doesn't have "t" as a variable. I have also tried θ-θi=1/2(ωi+ω)t. But that didn't end up taking the radius or mass into consideration.

The Attempt at a Solution



More or less stated in the relevant equations. This is due in a few hours, so anything is much appreciated. Thank you in advance!
 
Physics news on Phys.org
  • #2
Moment of inertia of the sphere is 2MR^2/5 and v = R*w.
So the rotational kinetic energy is given by 1/2*I*w^2 = 1/2*2M*R^2/5*v^2/R^2 = M*v^2/5.
And h = 1/2*g*sin(theta)*t^2.
Substitute these values in the relevant equation to solve for t.
 

What is the purpose of rolling a ball down a slope at a specific time?

The purpose of rolling a ball down a slope at a specific time is to study the relationship between time and distance. By measuring the time it takes for the ball to roll down the slope, scientists can calculate the acceleration due to gravity and other important factors related to motion.

How do you measure the time it takes for the ball to roll down the slope?

The time it takes for the ball to roll down the slope can be measured using a stopwatch or a timing device. The timer should be started as soon as the ball is released from the top of the slope and stopped once it reaches the bottom.

What factors can affect the time it takes for the ball to roll down the slope?

The time it takes for the ball to roll down the slope can be affected by various factors such as the slope angle, the surface of the slope, air resistance, and the mass of the ball. These factors can influence the acceleration and speed of the ball, ultimately affecting the time it takes to reach the bottom of the slope.

What is the significance of conducting this experiment at a specific time?

The specific time at which the experiment is conducted can provide valuable information about the influence of external factors on the motion of the ball. For example, conducting the experiment at different times of the day can reveal the impact of air resistance due to changing wind conditions.

What are the potential sources of error in this experiment?

The potential sources of error in this experiment include human error in timing the ball, variations in the slope surface, and air resistance. To minimize these errors, scientists must ensure precise measurements and conduct the experiment multiple times to obtain an average result.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Introductory Physics Homework Help
Replies
32
Views
2K
Replies
10
Views
441
  • Introductory Physics Homework Help
Replies
1
Views
752
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
208
  • Introductory Physics Homework Help
Replies
34
Views
704
  • Introductory Physics Homework Help
Replies
8
Views
1K
Replies
39
Views
2K
  • Introductory Physics Homework Help
Replies
12
Views
1K
Back
Top