In an ore-mixing operation, a bucket full of ore is suspended from a traveling crane which moves along a stationary bridge. the bucket is to swing no more than 20 ft horizontally when the crane is brought to a sudden stop. determine the maximum allowable speed v of the crane. (round the final answer to two decimal places.

To solve the problem, you should first convert the 20ft to meters so it is much easier.

20 feet is equals to 6 meters; rounded off to the nearest whole number.

Solution:

V1 = v

V2 = 0

T1 = ½ mv^2

T2 – 0

U 1-2 = -mgh

d = 6m

--AB^2 = (10m)^2 = d^2 + y^2 = (6m)^2 = y^2

Y^2 = 100 – 36 = 64

Y = sqrt64

h = 10 – y = 10 – sqrt64 = 10 – 8 = 2 m

U 1- 2 = -m (9.81) (2) = -19.62

T1 + U1-2 = T2

1/2mv^2 – 19.62m = 0

v^2 = (2) (19.62) = 39.24

see earlier