Calculating Particle Speed on a Moving Sphere: Integration Method

Click For Summary
SUMMARY

The discussion focuses on calculating the speed of a particle released from the top of a moving sphere with radius R, which accelerates at a constant rate a. The speed is derived as a function of the angle θ with respect to the upward vertical, utilizing integration methods. The final expression for the particle's speed is given by the formula √(2R(a*sin θ + g - g*cos θ)). Participants emphasize the importance of incorporating horizontal pseudo force, normal reaction, and gravitational force in the calculations.

PREREQUISITES
  • Understanding of classical mechanics, specifically forces acting on a particle.
  • Familiarity with integration techniques in physics.
  • Knowledge of pseudo forces in non-inertial reference frames.
  • Basic principles of kinematics and dynamics.
NEXT STEPS
  • Study the application of integration in classical mechanics problems.
  • Learn about pseudo forces and their effects in accelerating frames of reference.
  • Explore advanced kinematics involving rotational motion and forces.
  • Investigate the implications of gravitational forces on moving objects in different contexts.
USEFUL FOR

Physics students, educators, and professionals interested in mechanics, particularly those focusing on motion dynamics and integration methods in problem-solving.

troy611
Messages
11
Reaction score
0
A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a particle is released from the top of sphere as soon as the sphere starts accelerating (i.e. at time = 0). Find the speed of the particle with respect to the sphere as a function of angle it makes with the upward vertical (take it as \theta)

hint: integration is to be used

i am just missing one term in the answer, i have taken, the horizontal pseudo force, Normal reaction, and weight of particle amd then used COE.

ps: answer is \sqrt{2R(a*sin theta + g - g*cos theta)}
 
Physics news on Phys.org
Hi troy611! :wink:

Show us your full calculations, and then we'll see what's missing, and we'll know how to help! :smile:
 

Similar threads

Undergrad Launching a particle at the highest point inside a sphere
  • · Replies 2 ·
Replies
2
Views
1K
Triple integral to find the gravity inside a solid sphere
  • · Replies 7 ·
Replies
7
Views
8K
2 sphere system, Conservation of Energy and Momentum
  • · Replies 59 ·
2
Replies
59
Views
6K
An accelerating sphere with a particle on it
  • · Replies 2 ·
Replies
2
Views
3K
Dynamics - particle moves on smooth inside surface of hemisphere?
  • · Replies 6 ·
Replies
6
Views
3K
Pressure exerted by water on Sphere partially exposed at end
  • · Replies 10 ·
Replies
10
Views
4K
Relative motion,work and energy
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Einstein brother-in-law elevator
  • · Replies 11 ·
Replies
11
Views
2K
Energy Dissipated: Calculate Rate in Joules/sec
  • · Replies 1 ·
Replies
1
Views
2K
What is the Direction of Friction on a Sphere Placed on a Smooth Inclined Plane?
  • · Replies 7 ·
Replies
7
Views
3K