Answer:
The work required to stretch a spring 12 ft beyond its natural length is 432 ft-lb
Explanation:
The work to stretch a spring is calculated using the formula:
Equation (1)
W = work in ft-lb
k = spring constant in lb/ft
x = spring deformation in ft
we clear k from the equation (1)
Equation (2)
We replace x = 2ft, W = 12 ft-lb in the equation (2)
Calculation of work required to stretch spring 12 ft
We replace k = 6 lb/ft and x = 12ft in the equation (1)
The correct answer would be C because declining a break from exercise is considered overload.
The law of conservation of momentum says that the total momentum in the system before and after the collision remains the same. Remember that <em>p = mv </em>(where p is momentum, m is mass, and v is velocity). To find the total momentum in the system, add up the momentum of each component.
Before the collision:
The momentum of the first cart is m*v = 1.5 * 1.2 = 1.8.
The momentum of the second cart is m*v = 0.75 * 0 = 0.
The total momentum is 1.8.
After the collision:
(where x is the unknown velocity):
The momentum of the first cart is m*v = 1.5x
The momentum of the second card is m*v = 0.75 * 2 = 1.5.
The total momentum is 1.5x + 1.5. Because of conservation of momentum, you know this is equal to the momentum before the collision:
1.8 = 1.5x + 1.5
Subtracting 1.5 from both sides:
0.3 = 1.5x
And dividing by 1.5:
x = 0.2 m/s forward (you know it is forward because it is positive)
What a delightful little problem !
Here's how I see it:
When 'C' is touched to 'A', charge flows to 'C' until the two of them are equally charged. So now, 'A' has half of its original charge, and 'C' has the other half.
Then, when 'C' is touched to 'B', charge flows to it until the two of <u>them</u> are equally charged. How much is that ? Well, just before they touch, 'C' has half of an original charge, and 'B' has a full one, so 1/4 of an original charge flows from 'B' to 'C', and then each of them has 3/4 of an original charge.
To review what we have now: 'A' has 1/2 of its original charge, and 'B' has 3/4 of it.
The force between any two charges is:
F = (a constant) x (one charge) x (the other one) / (the distance between them)².
For 'A' and 'B', the distance doesn't change, so we can leave that out of our formula.
The original force between them was 3 = (some constant) x (1 charge) x (1 charge).
The new force between them is F = (the same constant) x (1/2) x (3/4) .
Divide the first equation by the second one, and you have a proportion:
3 / F = 1 / ( 1/2 x 3/4 )
Cross-multiply this proportion:
3 (1/2 x 3/4) = F
F = 3/2 x 3/4 = 9/8 = <em>1.125 newton</em>.
That's my story, and I'm sticking to it.