Question

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.

Answer 1

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