Forces - Acceleration, Polar Coordinates
A block of mass m = 2 kg is located
at a constant distance R = 0.3 m from point A as shown in the figure.
The bar (with the block of mass m on top) is rotating around point A in
starting (t=0) at Θ=0. The angle Θ varies in time according
Θ = ½ α * t² with α=10 rad/sec²
Your task is to investigate the fate of the block when θ = 1 rad ( about
57.296°). To this end :
- Determine the value of time t at which the rod arrives at
Θ = 1 rad. Also determine dΘ/dt, and d²Θ/dt² for the same point in time.
- Determine the radial and tangential force necessary to keep the mass
moving on its circular arc at that point in time
when θ = 1 rad ( about 57.296° ). Base these calculations on
the value of the angular velocity and acceleration you determined
under point (1).
- Draw a free-body-diagram of the mass m. Enter the action of the
bar onto the mass in terms of a normal and a friction
force. Take a minute to decide on the direction of the friction force
by considering which direction (inward or outward) the block is in danger
of sliding according to the results of point (2) and the action
- Question : If μ=0.32 between block and rotating arm, will
the block slide and if yes in which direction ?
Assume g = 9.81 m/s².