3/46 A "swing ride" is shown in the figure. Calculate the necessary angular velocity ω for the swings to assume an angle θ = 35∘ with the vertical. Neglect the mass of the cables and treat the chair and person as one particle. PROBLEM 3/46
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3/46 A "swing ride" is shown in the figure. Calculate the necessary angular velocity for the swings to assume an angle with the vertical. Neglect the mass of the cables and treat the chair and person as one particle.
PROBLEM
![A uniform meter-stick of mass M = 10 kg is hanging with the support of a hinge A and a cable at an angle θ = 45∘ as shown in the figure below. If the block of mass m = 8 kg moves beyond x = 0.73 m from hinge A, the cable breaks. Find the maximum tension T the cable can withstand. [5 Pts]With the block placed at x = 0.5 m, what are the horizontal and vertical components of the force on the bar from hinge A ? [10 Pts] Suppose the block of mass m is now at x = 0.74 m and the cable breaks, what is the angular acceleration of the system right after the cable breaks (You can assume that the block is a point mass)? [5 Pts]](https://www.doubtrix.com/uploads/editor/0757302795irIJrPKLHL.png)
![A 50 kg child stands on the edge of a stationary thin rod of length 5.0 m and mass M = 100 kg, free to rotate around its center of mass O. The child catches a ball of mass 2.0 kg thrown by a friend. Just before the ball is caught, the ball has a horizontal velocity of magnitude 30 ms−1, at angle θ = π/4 with a rod, as shown in Fig. 4 (a) What is the angular speed of the thin rod just after the ball is caught? (b) What is the mechanical energy of the child after the ball has been caught? [6 marks] (c) With what horizontal velocity, at an angle ϕ = π/6 with respect to the rod, has the boy to throw away the ball such that after the launch he will stay at rest? [7 marks]](https://www.doubtrix.com/uploads/editor/9895436237ysrDMhQJnq.png)