An ancient and deadly weapon, a sling consists of two braided cords, each about
ID: 2278028 • Letter: A
Question
An ancient and deadly weapon, a sling consists of two braided cords, each about half an arm's length long, attached to a leather pocket. The pocket is loaded with a projectile made of lead, carved rock, or clay and made to swing in a vertical circle as shown in the figure below. The projectile is released by letting go of one end of the cord. (Assume the radius of the circle the sling makes is 1.0 m.)
(a) If a Roman soldier can swing the sling at a rate of 6.5 rotations per second, what is the maximum range of his 109-g projectile? (Ignore air drag.)
(b) What is the maximum tension in each cord during the rotation?
A popular circus act features daredevil motorcycle riders encased in the "Globe of Death" (see the figure below), a spherical metal cage of diameter 17 ft. Assume a speed of 25 mi/h for both tricks.
(a) A rider of mass 68 kg on a 125-cc (95-kg) motorcycle keeps his bike horizontal as he rides around the "equator" of the globe. What coefficient of friction is needed between his tire and the cage to keep him in place?
(b) How many loops will the rider make per second?
(c) The same rider performs vertical loops in the globe. What force does the cage need to withstand at the top and the bottom of the rider's loop?
F top=
F bottom=
An ancient and deadly weapon, a sling consists of two braided cords, each about half an arm's length long, attached to a leather pocket. The pocket is loaded with a projectile made of lead, carved rock, or clay and made to swing in a vertical circle as shown in the figure below. The projectile is released by letting go of one end of the cord. (Assume the radius of the circle the sling makes is 1.0 m.) If a Roman soldier can swing the sling at a rate of 6.5 rotations per second, what is the maximum range of his 109-g projectile? (Ignore air drag.) What is the maximum tension in each cord during the rotation? A popular circus act features daredevil motorcycle riders encased in the "Globe of Death" (see the figure below), a spherical metal cage of diameter 17 ft. Assume a speed of 25 mi/h for both tricks. A rider of mass 68 kg on a 125-cc (95-kg) motorcycle keeps his bike horizontal as he rides around the "equator" of the globe. What coefficient of friction is needed between his tire and the cage to keep him in place? How many loops will the rider make per second? The same rider performs vertical loops in the globe. What force does the cage need to withstand at the top and the bottom of the rider's loop?Explanation / Answer
radius is 1 m
max vel = 13 pi m/s = 40.84m/s
max range = u^2 / g = 170.194 m
max tension = m u^2/r = 195.14 N
2)
A) for biker to be in horizontal position
friction force = mg
(mu)N = mg and N = cenrigugal force = mv^2/r
(mu)mv^2/r = mg
(mu) = gr/v^2 = 9.8 x 2.6 /(10.28^2) = 0.24
coefficient of friction = 0.24
B) v = wr
w = 3.95 rad/s
0.62 revolution per second
C)Ftop = mv^2/r - mg = 5058.66 N
Fbottom = mv^2/r + mg= 8273.06 N
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