The force F required to stretch a string varies directly with the amount the string is stretched, S. 32 pounds is needed to stretch a string 4 inches..
A) Write a direct variation equation that relates F and S.
Answer: 32=F*S+4 is what I think.. Most likely wrong.
B) How much force is required to stretch a string 20 inches?
Answer: well, first. I would need to have my equation right.
What I think I need help with: Could I please have somebody help me fix my equation so I could solve for B? Cause I don't think my equation is right.
Thanks!
Allyson.
A: force= constant*distance
constant= force/distance= 32/4 in pounds/inch
B: Force= (32/4)*20
Thank you.
To write a direct variation equation relating force (F) and the amount the string is stretched (S), we know that "the force required to stretch a string varies directly with the amount the string is stretched." This can be written as:
F = k * S
Where k is the constant of variation.
In order to solve for k, we are given that 32 pounds is needed to stretch the string 4 inches. We can use this information to find the value of k.
32 = k * 4
To solve for k, divide both sides of the equation by 4:
k = 32/4 = 8
Now that we have the value of k as 8, we can use it in our equation to solve part B.
B) How much force is required to stretch a string 20 inches?
F = k * S
F = 8 * 20
F = 160 pounds
Therefore, 160 pounds of force is required to stretch the string 20 inches.
Let me know if you need any further explanation or assistance!