A particle of mass M = 150 g lies, initially at rest, on a fixed horizontal...

   

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A particle of mass M₂ = 150 g lies, initially at rest, on a fixed horizontal plane with no friction. The particle M₂ is connected to another one, of mass M₁ = 200 g. by an ideal wire, inextensible and of zero mass, which passes through a hole in the plane as in the figure below. The particle M₁ is connected to the floor by a spring. When the particle M₂ is at rest the spring is compressed by a length Azo = 19.6 cm. At time t = 0 the particle M₂ is kicked in a direction perpendicular to the wire, in a way that it starts rotating without putting particle M₁ into oscillation. Particle M₂ starts rotating around the hole with a circular trajectory of radius R = 25 cm and angular frequency f = 0.5 turns/s. Olery M₁ M₂ (a) What is the tension exerted by the wire on particle M₂ before time t = 0? (b) What is the spring constant? (c) After t = 0, is the spring compressed or extended? Find the value of this quantity, AT1. (d) What is the total mechanical energy after time t = 0? The particle M₂ is at 1 m height over the floor. The resting length of the spring is 0.3 m. (e) At time t = t₁ sand is poured on the top plane to induce friction. After having travelled for a trajectory of length d = 39 cm in a spiral trajectory, the particle M₂ goes to rest on the plane. At this moment the spring compression is measured to be Ar2 = 18 cm. How much is the dynamic friction coefficient up between M₂ and the plane? A particle of mass M₂ = 150 g lies, initially at rest, on a fixed horizontal plane with no friction. The particle M₂ is connected to another one, of mass M₁ = 200 g. by an ideal wire, inextensible and of zero mass, which passes through a hole in the plane as in the figure below. The particle M₁ is connected to the floor by a spring. When the particle M₂ is at rest the spring is compressed by a length Azo = 19.6 cm. At time t = 0 the particle M₂ is kicked in a direction perpendicular to the wire, in a way that it starts rotating without putting particle M₁ into oscillation. Particle M₂ starts rotating around the hole with a circular trajectory of radius R = 25 cm and angular frequency f = 0.5 turns/s. Olery M₁ M₂ (a) What is the tension exerted by the wire on particle M₂ before time t = 0? (b) What is the spring constant? (c) After t = 0, is the spring compressed or extended? Find the value of this quantity, AT1. (d) What is the total mechanical energy after time t = 0? The particle M₂ is at 1 m height over the floor. The resting length of the spring is 0.3 m. (e) At time t = t₁ sand is poured on the top plane to induce friction. After having travelled for a trajectory of length d = 39 cm in a spiral trajectory, the particle M₂ goes to rest on the plane. At this moment the spring compression is measured to be Ar2 = 18 cm. How much is the dynamic friction coefficient up between M₂ and the plane?

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a Before time t 0 when particle M is at rest the tension in the wire is equal to the centripetal force required to keep particle M moving in a circula... View the full answer