Problem # p024

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 counter-clockwise direction starting (t=0) at Θ=0. The angle Θ varies in time according to :

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 :

  1. 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.

  2. 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).

  3. 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 of gravity.

  4. 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.