Question

A wheel has eight spokes and a radius of 30 cm. It is mounted on a fixed axle and is spinning at 2.5 rev/s. You want to shoot a 24- cm arrow parallel to this axle and through the wheel without hitting any of the spokes Assume that the arrow and the spokes hitting any of the spokes. Assume that the arrow and the spokes are very thin. (a) What minimum speed must the arrow have to pass through (a) What minimum speed must the arrow have to pass through without contact

Answer 1

Answer:

4.8 m/s

Explanation:

Given: angular velocity of wheel ω = 2.5 rev/sec

radius r = 30 cm

length of arrow = 24 cm

For arrow to pass through spinning ring it has to pass between any two spokes of the wheel.

angle between two spokes = π/4

time taken by a spook to reach the position of adjacent spoke t =θ/ω

=  π/4/(2.5×2π) = 1/20 sec

for the arrow to pass through the spokes of the wheel it should take time t <1/20 sec to pass through the wheel

a) therefore, minimum speed = (24/100)/(1/20) = 4.8 m/s