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Tema [17]
3 years ago
14

Hooke's law describes a certain light spring of unstretched length 34.8 cm. When one end is attached to the top of a doorframe a

nd a 8.22 kg object is hung from the other end, the length of the spring is 40.8 cm. (a) Find its spring constant. 1342.6 kN/m (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 205 N. Find the length of the spring in this situation. m
Physics
1 answer:
DaniilM [7]3 years ago
6 0

Answer:

a) k = 1343.6\,\frac{N}{m}, b) l = 0.501\,m\,(50.1\,cm)

Explanation:

a) The Hooke's law states that spring force is directly proportional to change in length. That is to say:

F \propto \Delta l

In this case, the force is equal to the weight of the object:

F = m\cdot g

F = (8.22\,kg)\cdot (9.807\,\frac{m}{s^{2}} )

F = 80.614\,N

The spring constant is:

k = \frac{F}{\Delta l}

k = \frac{80.614\,N}{0.408\,m-0.348\,m}

k = 1343.6\,\frac{N}{m}

b) The length of the spring is:

F = k\cdot (l-l_{o})

l = l_{o} + \frac{F}{k}

l=0.348\,m+\frac{205\,N}{1343.6\,\frac{N}{m} }

l = 0.501\,m\,(50.1\,cm)

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