How Fast Can a Child Swing Without Breaking the Rope?

[ELE55AR]

I got this 2 problems, and final solutions.
What I need is the build up, or in other words: EVERYTHING!

please HELP!4.17.
The child swings on a rope that is 4 m (meters) long. If the tension of the rope increases to the amount that is double the weight of the child, the rope will break. What is the highest speed with which the child can pass through the lowest position of the orbit(path/trajectory)?
(Final solution: v=$$\sqrt{\frac{g}{L}}$$)4.28.
Motorcycle with the driver, total weighing 180 kg, is crossing the circle-shaped arched bridge, with radius of 20 m, at average speed 36 km/h.
Calculate the force that wheels of motorcycle are pressing on the bridge while going over it?
(sorry for bad english at this one, but you'll get it)

(Final solution: F= 865,8 N)

 

[rock.freak667]

4.17.
The child swings on a rope that is 4 m (meters) long. If the tension of the rope increases to the amount that is double the weight of the child, the rope will break. What is the highest speed with which the child can pass through the lowest position of the orbit(path/trajectory)?



(Final solution: v=$$\sqrt{\frac{g}{L}}$$)

I don't think this is correct, since sqrt(g/L) does not give units of m/s.

But if the child is moving in a circular orbit, what forces are acting at the lowest point? What do the resultant of these two give?

4.28.
Motorcycle with the driver, total weighing 180 kg, is crossing the circle-shaped arched bridge, with radius of 20 m, at average speed 36 km/h.
Calculate the force that wheels of motorcycle are pressing on the bridge while going over it?
(sorry for bad english at this one, but you'll get it)

(Final solution: F= 865,8 N)

Once again, what are the forces acting on the motorcycle as it is going over the circular arch?

(Remember your formulas from circular motion for the two problems)