Work and spring constant questions?

In summary, the man lifted a 11.0 kg bucket from a well and did 7.00 kJ of work. Using the equation work = fd, the force required to lift the mass is 107.91 N. Assuming the speed of the bucket remains constant, the depth of the well is approximately 64.87 m. For the Hooke's Law problem, we can use the equation PE = (1/2)k(x^2) to find the spring constant and the force equation, f = ma, to find the displacement of the spring in a different situation.
  • #1
bbanas0695
3
0
1) If a man lifts a 11.0 kg bucket from a well and does 7.00 kJ of work, how deep is the well? Assume that the speed of the bucket remains constant as it is lifted.

2) Hooke's law describes a certain light spring of unstretched length 36.0 cm. When one end is attached to the top of a door frame, and a 7.60-kg object is hung from the other end, the length of the spring is 45.50 cm.

(a) Find its spring constant.
(b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 170 N. Find the length of the spring in this situation.
work=fd
PE=(1/2)k(x^2)
ok for the first one i did 7000J/11= 636.36 and it says that's wrong
and for the second one I am not even sure where to start
 
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  • #2
bbanas0695 said:
1) If a man lifts a 11.0 kg bucket from a well and does 7.00 kJ of work, how deep is the well? Assume that the speed of the bucket remains constant as it is lifted.

work=fd


ok for the first one i did 7000J/11= 636.36 and it says that's wrong

You are using the correct equation, work = fd. So, what is f, the force required to lift a mass of 11 kg? Hint: it is the same as the force of gravity exerted on the mass.

2) Hooke's law describes a certain light spring of unstretched length 36.0 cm. When one end is attached to the top of a door frame, and a 7.60-kg object is hung from the other end, the length of the spring is 45.50 cm.

(a) Find its spring constant.
(b) The load and the spring are taken down. Two people pull in opposite directions on the ends of the spring, each with a force of 170 N. Find the length of the spring in this situation.


PE=(1/2)k(x^2)
There is another useful equation for springs, relating force and displacement (amount of stretch) of the end of the spring. Find that equation and try to apply it here.
 
  • #3
You are using the correct equation, work = fd. So, what is f, the force required to lift a mass of 11 kg? Hint: it is the same as the force of gravity exerted on the mass.

the force of gravity is 9.81 so that would be the force. so 7000/9.81= 713.56 m ?

and for the second one, i guess we don't have to do it. the answer in the website is wrong or something.
 
  • #4
oh wait. you need to find force using f=ma so 11*9.81=107.91
and then plug that in which would be 7000/107.91= 64.87m
i already got it wrong on the homework but thanks. At least I know how to do it now :)
 
  • #5
bbanas0695 said:
oh wait. you need to find force using f=ma so 11*9.81=107.91
and then plug that in which would be 7000/107.91= 64.87m
i already got it wrong on the homework but thanks. At least I know how to do it now :)
Looks good. Too late for the homework, but remember it for the test :smile:
 

FAQ: Work and spring constant questions?

What is work and how is it related to spring constant?

Work is the amount of energy expended by a force on an object to move it a certain distance. In the context of spring constant, work is the force applied to stretch or compress a spring multiplied by the distance the spring moves. This relationship is known as Hooke's Law.

How is the spring constant calculated?

The spring constant is calculated by dividing the force applied to a spring by the resulting displacement of the spring. It is represented by the letter k and has units of Newtons per meter (N/m).

What factors affect the spring constant?

The spring constant is affected by the material of the spring, the thickness and length of the spring, and the number of coils in the spring. Generally, stiffer materials and shorter, thicker springs will have a higher spring constant.

How does the spring constant affect the behavior of a spring?

The spring constant determines the stiffness of a spring, meaning how much force is required to stretch or compress the spring. A higher spring constant means a stiffer spring that requires more force to move and has a smaller displacement. A lower spring constant means a more flexible spring that requires less force to move and has a larger displacement.

Can the spring constant of a spring change?

Yes, the spring constant can change depending on various factors such as temperature, material fatigue, and damage to the spring. Additionally, different springs can have different spring constants even if they are made of the same material, due to variations in manufacturing processes.

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