Question 1

The force ($F$ newtons) applied to a spring is directly proportional to its extension ($x$ cm).
When F=120, $x=8$ cm.

(a) Find a formula for F in terms of $x$.
F= 

(b) Calculate F when $x=20$ cm.  F = N

 

---

Question 2

The tension (T N) in a wire is directly proportional to its extension ($x$ cm).
When $T=200$ N, $x=10$ cm.

(a) Find $T$ in terms of $x$. T =
(b) Find $T$ when $x=25$ cm. T = N

 

---

Question 3

The weight ($W$ kg) of a hanging object stretches a spring by $x$ cm.
When $W=75$ kg, $x=5$ cm.

(a) Express $W$ in terms of $x$. W =
(b) Find $W$ when $x=12$ cm. W = Kg

 

---

Question 4

The force ($F$ N) needed to stretch a rope is directly proportional to its elongation ($x$ cm).
When $F=90$ N, $x=3$ cm.

(a) Find $F$ in terms of $x$. F =
(b) Find $F$ when $x=9$ cm. F = N

 

---

Question 5

The restoring force ($R$ N) in a stretched material is proportional to its extension ($x$ cm).
When $R=50$ N, $x=2.5$ cm.

(a) Express $R$ in terms of $x$. R =
(b) Find $R$ when $x=10$ cm. R = N

 

---

Question 6

The length ($L$ cm) of a stretched rubber band is proportional to the force ($F$ N) applied.
When $L=30$ cm, $F=5$ N.

(a) Express $L$ in terms of $F$. F =
(b) Find $L$ when $F=12$ N. F = cm

 

---

Question 7

The force ($F$ N) exerted by a stretched spring is proportional to its extension ($x$ cm).
When $F=45$ N, $x=3$ cm.

(a) Express $F$ in terms of $x$. F =
(b) Find $F$ when $x=12$ cm. F = N

 

---

Question 8

The weight ($W$ kg) of an object compresses a spring by $x$ cm.
When $W=180$ kg, $x=9$ cm.

(a) Express $W$ in terms of $x$. W =
(b) Find $W$ when $x=15$ cm.W = Kg

 

---

Question 9

The force ($F$ N) required to extend a rope is proportional to its extension ($x$ cm).
When $F=250$ N, $x=25$ cm.

(a) Express $F$ in terms of $x$. F =
(b) Find $F$ when $x=50$ cm. F = N 

 

---

Question 10

The load ($L$ kg) applied to a spring stretches it by $x$ cm.
When $L=90$ kg, $x=6$ cm.

(a) Express $L$ in terms of $x$. L =
(b) Find $L$ when $x=18$ cm.   L = kg

Solution:

(a) $L=kx$, so

$$90=k(6)\Rightarrow k=15$$

Thus, $L=15x$.

(b) When $x=18$:

$$L=15(18)=270\text{ kg}$$