Answer:
5,760,000 lb-ft²/s²
Explanation:
Work done, W = mgy where m = mass of stone = 12,000 lb, g = 32 ft/s² and y = vertical distance = 15 ft.
So, W = mgy = 12,000 lb × 32 ft/s² × 15 ft. = 5,760,000 lb-ft²/s²
Answer:
Both objects travel the same distance.
(c) is correct option
Explanation:
Given that,
Mass of first object = 4.0 kg
Speed of first object = 2.0 m/s
Mass of second object = 1.0 kg
Speed of second object = 4.0 m/s
We need to calculate the stopping distance
For first particle
Using equation of motion

Where, v = final velocity
u = initial velocity
s = distance
Put the value in the equation

....(I)
Using newton law

Now, put the value of a in equation (I)

Now, For second object
Using equation of motion

Put the value in the equation

....(I)
Using newton law


Now, put the value of a in equation (I)

Hence, Both objects travel the same distance.
Answer:
W = 68 J
Explanation:
On a force vs displacement chart, work is the area under the curve.
The area under the curve can be divided into a rectangle and a triangle
W = Fd = (2 N)(12 - 0 m) + ½(13 - 2 N)(12 - 4 m) = 68 N•m = J
Answer:
The potential energy is transformed into kinetic energy
Explanation:
This particular case is defined as the principle of energy conservation since energy is not created or destroyed only transforms. When you have potential energy it can be transformed into kinetic energy or vice versa. In this problem, we have the case of a ball that sits on a desk and then falls to the ground. In this way the ground will be taken as a reference point, this is a point at which the potential energy will be equal to zero in such a way that when the ball is on the desktop that is above the reference line its potential energy will be maximum. As the ball drops its potential energy decreases, as the height relative to the ground (reference point) decreases. In contrast its kinetic energy increases and increases as it approaches the ground. So when it hits the ground it will have maximum kinetic energy and will be equal to the potential energy for when the ball was on the desk.
Therefore:
![E_{p} = potential energy [J] = E_{k} = kinetic energy [J]where:\\E_{p} =m*g*h\\m =mass [kg]\\g=gravity[m/s^2]\\h=elevation[m]\\E_{k} = \frac{1}{2} *m*v^{2} \\where:\\v=velocity [m/s]\\\frac{1}{2} *m*v^{2} = m*g*h](https://tex.z-dn.net/?f=E_%7Bp%7D%20%3D%20potential%20energy%20%5BJ%5D%20%3D%20E_%7Bk%7D%20%3D%20kinetic%20energy%20%5BJ%5Dwhere%3A%5C%5CE_%7Bp%7D%20%3Dm%2Ag%2Ah%5C%5Cm%20%3Dmass%20%5Bkg%5D%5C%5Cg%3Dgravity%5Bm%2Fs%5E2%5D%5C%5Ch%3Delevation%5Bm%5D%5C%5CE_%7Bk%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2Am%2Av%5E%7B2%7D%20%5C%5Cwhere%3A%5C%5Cv%3Dvelocity%20%5Bm%2Fs%5D%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%20%2Am%2Av%5E%7B2%7D%20%3D%20m%2Ag%2Ah)
Answer:
376966.991 Joules
Explanation:
Given that :
the height = 12 m
Let assume the tank have a thickness = dh
The radius of the tank by using the concept of similar triangle is :


The area of the tank =
The area of the tank = 
The area of the tank = 
The volume of the tank is = area × thickness
= 
Weight of the element = 
where;
= density of water ; which is given as 10000 N/m³
So;
Weight of the element = 
Weight of the element = 
However; the work required to pump this water = weight × height rise
where the height rise = 12 - h
the work required to pump this water =
(12 - h)
the work required to pump this water = 
We can determine the total workdone by integrating the work required to pump this water
SO;
Workdone = 
= 
= ![\mathbf{ 69.44 \pi[ \frac{12h^3}{3}- \frac{h^4}{4}]^{12}}_0} }](https://tex.z-dn.net/?f=%5Cmathbf%7B%2069.44%20%5Cpi%5B%20%5Cfrac%7B12h%5E3%7D%7B3%7D-%20%20%5Cfrac%7Bh%5E4%7D%7B4%7D%5D%5E%7B12%7D%7D_0%7D%20%7D)
= ![\mathbf{69.44 \pi [ \frac{12^4}{3}-\frac{12^4}{4}]}](https://tex.z-dn.net/?f=%5Cmathbf%7B69.44%20%5Cpi%20%5B%20%5Cfrac%7B12%5E4%7D%7B3%7D-%5Cfrac%7B12%5E4%7D%7B4%7D%5D%7D)
= ![\mathbf{69.44 \pi*12^4 [ \frac{4-3}{12}]}](https://tex.z-dn.net/?f=%5Cmathbf%7B69.44%20%5Cpi%2A12%5E4%20%5B%20%5Cfrac%7B4-3%7D%7B12%7D%5D%7D)
= 
= 376966.991 Joules