Force, distance, and a constant

[Jdpaul88]

Homework Statement

As an exercise, a woman pulls on both sides of a stiff spring to work on her chest muscles. The spring stretches 7.2 cm when she pulls on it with a force of 111 N. She then makes a greater effort and stretches the spring 17 cm.

a. Write an equation relating the force, F, with which the spring is pulled, the distance the spring is pulled, x, and the spring constant K.

b. What is the spring constant in this case?

c. What force would be necessary to stretch the spring 17 cm?

Homework Equations

The Attempt at a Solution

For the equation, I came up with x=Fk. Now to find the constant, I took x/F=K. I got 0.06486 and just rounded to 0.06 for the sake of significant figures. After that, I took x/k=F to get the force used to stretch it 17 cm. 17/0.06=280 N. Does this sound correct?

 

[LowlyPion]

Homework Statement

As an exercise, a woman pulls on both sides of a stiff spring to work on her chest muscles. The spring stretches 7.2 cm when she pulls on it with a force of 111 N. She then makes a greater effort and stretches the spring 17 cm.

a. Write an equation relating the force, F, with which the spring is pulled, the distance the spring is pulled, x, and the spring constant K.

b. What is the spring constant in this case?

c. What force would be necessary to stretch the spring 17 cm?

Homework Equations

The Attempt at a Solution

For the equation, I came up with x=Fk. Now to find the constant, I took x/F=K. I got 0.06486 and just rounded to 0.06 for the sake of significant figures. After that, I took x/k=F to get the force used to stretch it 17 cm. 17/0.06=280 N. Does this sound correct?

I think your equation is a little non traditional. Generally F would be expressed as x times a constant as in F= K*x. So long as you recognize that the K of this formula is 1/k in your formula that you used I think you are OK.

You could also avoid the issue of significant digits by observing that if k is constant that

$$\frac{x_1}{F_1} = \frac{x_2}{F_2}$$

$$\frac{7.2}{111} = \frac{17}{F_2}$$

 

[baba89]

Your approach to solving this problem is correct. The equation relating force, distance, and the spring constant is F = Kx, where F is the force applied, x is the distance the spring is stretched, and K is the spring constant. In this case, the spring constant is equal to 0.06, as you correctly calculated. This means that for every 1 cm the spring is stretched, a force of 0.06 N is applied. Therefore, to stretch the spring 17 cm, a force of 17 x 0.06 = 1.02 N is necessary. Overall, your solution is correct.