A solid 0.4750 kg ball rolls without slipping down a track toward a vertical loop of radius R = 0.7350 m. What minimum translational speed Umin must the ball have when it is a height H = 1.111 m above the bottom of the loop in order to complete the loop without falling off the track? Assume that the radius of the ball itself is much smaller 9.810 m/s? for the than the loop radius R. Use g = acceleration due to gravity.
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
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A solid 0.4750 kg ball rolls without slipping down a track
toward a vertical loop of radius R = 0.7350 m. What
minimum translational speed vmin must the ball have when
it is a height H = 1.111 m above the bottom of the loop in
order to complete the loop without falling off the track?
H
Assume that the radius of the ball itself is much smaller
than the loop radius R. Useg = 9.810 m/s² for the
acceleration due to gravity.
Figure is not to scale.
5.177
m/s
Umin =
Incorrect
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