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Write a system of equations to describe the situation below, solve using substitution, and fill in the
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Answer:
18 J is the work required to stretch a spring from 7 m to 13 m.
Step-by-step explanation:
The work done is defined to be the product of the force and the distance
that the object moves:
If is measured in newtons and
<em> </em>in meters, then the unit for is a newton-meter, which is called a joule (J).
This definition work as long as the force is constant, but if the force is variable like in this case, we have that the work done is given by
Hooke’s Law states that the force required to maintain a spring stretched units beyond its natural length is proportional to
where is a positive constant (called the spring constant).
To find how much work W is required to stretch it from 7 m to 13 m you must:
Step 1: Find the spring constant
We know that the spring has a natural length of 7 m and a 4 N force is required to keep it stretched to a length of 11 m. So, applying Hooke’s Law
Thus
Step 2: Find the the work done in stretching the spring from 7 m to 13 m.
Recall that the natural length is 7 m, so when we stretch the spring from 7 m to 13 m, we are stretching it by 6 m beyond its natural length.
Work needed to stretch it by 6 m beyond its natural length
18 J is the work required to stretch a spring from 7 m to 13 m.