Please complete the following problems (remember, you must use engineering paper

Question

Please complete the following problems (remember, you must use engineering paper). Make sure you report all answers with the correct number of significant digits. To remove any ambiguity in the given numbers a “trailing decimal point” (as in “50.”) tells you that the previous zeros are all significant.

A streambed has a slope of 0.00150 (dimensionless; or m/m or ft/ft, if you prefer.) What is the gravitational force in the “downstream” direction (in units of newtons) acting on a 1.00 m3 cube of water. (Hint: This is not the weight of the water; it’s the force that pulls the water down the stream bed). The water is 20°C so please use the correct water density for this temperature.

Explanation / Answer

Density of water at 200C is 998.23 kg/m3

So mass of cube of water = 998.23kg

Gravitational force acting on it in downward direction = mg sin A,

Where A is the angle of inclined plane with horizontal.

As slope = tan A = 0.00150/1 = perpendicular/base

Hence hypotenuse = {(0.00150)2 + (1)2}1/2= (0.000000225 + 1)1/2

= 1.0000001125

Hence sin A = 1/1.0000001125 = 0.99999988

Hence downward pull = 998.23 x 9.8 x 0.99999988

= 9782.6528N

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