Applied Mechanics and Graphic Statics
‘ω’ rad/sec is the angular velocity of a crank whose radius is ‘r’. If it makes θ° with inner dead centre and obliquity of the connecting rod ‘l’ is ‘ϕ’, the velocity v of the piston, is given by the equation

ω (l sin ϕ + r cos ϕ tan θ)
ω² (l sin ϕ - r cos θ tan ϕ)
ω² (l cos ϕ + r sin ϕ tan θ)
ω² (l sin ϕ + r cos φ tan θ)

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Applied Mechanics and Graphic Statics
‘u₁’ and ‘u₂’ are the velocities of approach of two moving bodies in the same direction and their corresponding velocities of separation are ‘v₁’ and ‘v₂’. As per Newton's law of collision of elastic bodies, the coefficient of restitution (e) is given by

e = v₂ - v₁/u₁ - u₂
e = v₁ - v₂/u₂ - u₁
e = v₁ - v₂/u₂ + u₁
e = u₂ - u₁/v₁ - v₂

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Applied Mechanics and Graphic Statics
A sphere and a cylinder having the same mass and radii start from rest and roll down the same inclined plane. Which body gets to the bottom first?

Both reach the bottom simultaneously with equal rotational energy at bottom
Sphere with greater rotational energy at bottom than cylinder
Sphere with lesser rotational energy at bottom than cylinder
Cylinder with greater rotational energy at bottom than sphere

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