The following exercise combines springs, oscillations, stability of a rigid body and rolling without slipping. It was the fourth exercise in the 2016 paper of physics in Greek National University entrance exams.
A block Σ having mass m=1 Kg is attached to the lower end of an ideal elastic spring of constant (stiffness) K=100 N/m. The upper end of the spring is attached to a firm point at the top a plane inclined at an angle φ=300 to the horizontal . The part BΓ of the inclined plane is smooth.
A block Σ having mass m=1 Kg is attached to the lower end of an ideal elastic spring of constant (stiffness) K=100 N/m. The upper end of the spring is attached to a firm point at the top a plane inclined at an angle φ=300 to the horizontal . The part BΓ of the inclined plane is smooth.
A solid homogeneous cylinder having
mass M=2Kg and radius R=0.1m is connected to the Block through a
massless and unstrechable cord. The cylinder's axis is horizontal.
The cord and the spring's axis are parallel to the inclined plane.
The system of all the bodies is initially at rest.
At t=0 the cord is broken. Block P
starts a simple harmonic oscillation while cylinder starts rolling
without slipping.
B1. write the formula that gives the
restoring force as a function of time. Take as positive the direction
towards the bottom of the inclined plane.
answer
answer
B3. Calculate the cylinder's kinetic
energy rate of change at t=3s.
The following information is given:
- the acceleration of gravity g=10m/s2
- the cylinders moment of inertia: I=0.5MR 2
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