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.

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Physics

4 December, 09:42

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.

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Deandre Ashley · 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