Chapter 5.2, Problem 43PPE

a.

To determine

To determine the ratio of force to weight for the lever.

Answer to Problem 43PPE

  $\frac{2}{5}$

Explanation of Solution

Given:

Force applied to a lever varies directly to the weight

Lifting $50$ lb weight by applying $20$ lb force

Calculation:

Let’s consider force as $F$ and weight as $w$ .

Now, consider the equation as,

  $\begin{array}{l}\Rightarrow F\propto w\\ \Rightarrow F=kw\end{array}$   [ $\because$ Function form of direct variation]

Now, $F=20$ lb and $w=50$ lb,

  $\Rightarrow 20=k\times 50$

  $\Rightarrow k=\frac{2}{5}$

Conclusion:

Therefore, the ratio of force to weight is $\frac{2}{5}$ .

b.

To determine

To determine equation relating force to weight for the lever and also find the force needed to lift a friend whose weight is 130 lb.

Answer to Problem 43PPE

  $F=\frac{2}{5}w$

  $52$ lb

Explanation of Solution

Given:

Force applied to a lever varies directly to the weight

Lifting $50$ lb weight by applying $20$ lb force

Weight is 130 lb

Calculation:

Let’s consider force as $F$ and weight as $w$ .

Now, consider the equation as,

  $\begin{array}{l}\Rightarrow F\propto w\\ \Rightarrow F=kw\end{array}$  [ $\because$ Function form of direct variation]

Now, $F=20$ lb and $w=50$ lb,

  $\Rightarrow 20=k\times 50$

  $\Rightarrow k=\frac{2}{5}$

Now putting the value of $k$ in $F=kw$ ,

  $\Rightarrow F=\frac{2}{5}w\to \text{(i)}$

Now putting the value of weight as $130$ lb in equation (i),

  $\Rightarrow F=\frac{2}{5}\times \text{130 }$

  $\Rightarrow F=52$ lb

Conclusion:

Therefore, the equation relating force to weight for the lever is $F=\frac{2}{5}w$ and the force needed to lift a friend whose weight is $130$ lb is $52$ lb.