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7.5 Apps from Science comp.notebook
1
November 26, 2019
Nov 271:15 PM
7.5 Applications from Science
WORK
In everyday life, work, means an activity that requires muscular or mental effort. In science, work, refers to a force acting on a body and the body’s subsequent displacement.
The constant work done formula is W=Fd
WhereW is the work doneF is the force appliedd is the distance moved in a straight line
Hooke’s Law for springs states that the force it takes to stretch or compress a spring x units from it’s natural (unstretched) length.
F=kx
F is the force appliedx is the distance movedk is the force constant measured in N/m
If the force is not constant, then the work done moving an object from a to b is given by:
Ex. 1 It takes a force of 10N to stretch a spring 2m beyond its
natural length. How much work is done stretching the spring 4m from its natural length?
Ex. 2 Find the work done by the force Newtons along the xaxis from x=0m to x=3m.
7.5 Apps from Science comp.notebook
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November 26, 2019
Nov 271:21 PM
Ex. 3 Work Done Lifting
A leaky bucket weighs 28N empty. It is lifted from the ground at a constant rate to a point 18m above ground by a rope weighing 0.8N/m. The bucket starts with 90N of water, but it leaks at a constant rate and just finishes draining just as it reaches the top. Find the amount of work done:
(a)Lifting the bucket alone(b)Lifting the water alone(c) Lifting the rope alone(d)Lifting the bucket, water and the rope together(e) Lifting the water alone, if the bucket is hauled up more quickly and there is still 10N water in the bucket.
7.5 Apps from Science comp.notebook
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November 26, 2019
Nov 2812:00 PM
Fluid Force and Fluid Pressure
Dams are built thicker at the bottom than the top because pressure against them increases with depth. The pressure at any point on a dam depends only on how far below the surface the point lies and not on how much water the dam is holding back. In any liquid, the fluid pressure p (force per unit area) at depth h is:
w is the weightdensity (weight per unit volume of the liquid).
Typical weight densities (lb/ft3):Gasoline 42 Mercury 849 Milk 64.5Molasses 100 Seawater 64 Water 62.4
Total Force on a constant depth surface is given by
where p = fluid pressure and A is the area in question.
Ex.4 Force
The vertical end of a tank containing water weighing 62.4 lb/ft3 has the shape below. Find the force as an integral and evaluate it.
Ex 4bFind the force if the liquid is filled to with in 2 feet of the top.
7.5 Apps from Science comp.notebook
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November 26, 2019
Nov 2812:00 PM
Ex.5 Work Done Pumping
A 10ft tall conical tank is filled to within 4 ft of the top with olive oil weighing 57 lb/ft3. How much work does it take to pump the oil to the rim of the tank?
7.5 Apps from Science comp.notebook
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November 26, 2019
Nov 2812:07 PM
Ex. 6 The Great Molasses Flood of 1919
At 1pm on January 15 1919 (an unreasonably warm day) in the north of Boston, a 90ft high, 90ft diameter cylindrical metal tank which contained molasses exploded. Molasses flooded streets 30ft deep, trapping pedestrians and knocking over horses, buildings and oozing into homes. It took weeks to clean up.
(a)Given the tank was full of molasses weighing 100lb/ft3, what was the total force exerted by the molasses on the bottom of the tank at the time it ruptured?(b) What was total force against the bottom footwide band of the wall?