Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m, and they are equally spaced by a distance d, as shown. The angles labeled θ describe the angle formed by the the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal labeled φ. Let T1 be the tension in the leftmost section of the string, T2 be the tension in the section adjacent to it, and T3 be the tension in the horizontal segment. a)Write an expression for T1 in terms of m, g, and θ b). Write an expression for T2 in terms of m, g, and θ . c) Write an expression for T3 in terms of m, g, and θ .
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).
Hanging from the ceiling over a baby bed, well out of baby’s reach, is a string with plastic shapes, as shown here. The string is taut (there is no slack), as shown by the straight segments. Each plastic shape has the same mass m, and they are equally spaced by a distance d, as shown. The angles labeled θ describe the angle formed by the the string and the ceiling at each end. The center length of sting is horizontal. The remaining two segments each form an angle with the horizontal labeled φ. Let T1 be the tension in the leftmost section of the string, T2 be the tension in the section adjacent to it, and T3 be the tension in the horizontal segment.
a)Write an expression for T1 in terms of m, g, and θ
b). Write an expression for T2 in terms of m, g, and θ .
c) Write an expression for T3 in terms of m, g, and θ .
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