Engineering Dynamics need help from 4,5,6,7 thank you A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°. Neglect any friction. Neglect also the size of the ball and the thickness of the arm. Find the relationship between r, R and θ where r is the distance between O and the ball. Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA. Write the equations of motion in the (r, θ) coordinate system. Find the normal force acting on the ball by the cylinder for Φ = Φ0. Find the normal force acting on the ball by the bar for Φ = Φ0. Determine the angle Φ at which the ball loses contact with the cylinder. Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°
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).
Engineering Dynamics need help from 4,5,6,7 thank you
A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant
Neglect any friction. Neglect also the size of the ball and the thickness of the arm.
- Find the relationship between r, R and θ where r is the distance between O and the ball.
- Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA.
- Write the equations of motion in the (r, θ) coordinate system.
- Find the normal force acting on the ball by the cylinder for Φ = Φ0.
- Find the normal force acting on the ball by the bar for Φ = Φ0.
- Determine the angle Φ at which the ball loses contact with the cylinder.
- Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°
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