Displayed to the right are two carts connected by a cord that passes over a small frictionless pulley. Each cart rolls freely with negligible friction. Consider the mass of the cart to be m1 and the angle the first cart sits on to be θ1, while the mass of the second cart as m2 and the angle it sits on to be θ2. a)Considering the positive x direction to be pointing as it is in the image, write an equation for the acceleration that the two blocks experience in terms of the mass of the first block m1, the angle θ1, the mass of the second block m2, the angle θ2, and the acceleration due to gravity g. b) What is the equation for tension in regards to the rope coming from the second block? Answer in terms of the mass of the block m2, the acceleration due to gravity g, the angle θ2, and the acceleration of the blocks found previously a.
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).
Displayed to the right are two carts connected by a cord that passes over a small frictionless pulley. Each cart rolls freely with negligible friction. Consider the mass of the cart to be m1 and the angle the first cart sits on to be θ1, while the mass of the second cart as m2 and the angle it sits on to be θ2.
a)Considering the positive x direction to be pointing as it is in the image, write an equation for the acceleration that the two blocks experience in terms of the mass of the first block m1, the angle θ1, the mass of the second block m2, the angle θ2, and the acceleration due to gravity g.
b) What is the equation for tension in regards to the rope coming from the second block? Answer in terms of the mass of the block m2, the acceleration due to gravity g, the angle θ2, and the acceleration of the blocks found previously a.
SOlution:
Given that
the mass of the cart to be m1 and the angle the first cart sits on to be θ1, while the mass of the second cart as m2 and the angle it sits on to be θ2.
To find the acceleration and tension equation
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