Question

problem 3
to open a jar of radius ( r = 3 ) cm, one needs to exert a force of 100 n. to make it easier, a wrench with a length of 14 cm from the center of the jar is used. what force needs to be used to open the jar with the wrench?

Explanation:

Step1: Calculate the torque without wrench

Torque formula is \( \tau = F\times r\).
Given \(F = 100\space N\) and \(r=3\space cm = 0.03\space m\).
\(\tau=100\times0.03\)
\(\tau = 3\space N\cdot m\)

Step2: Calculate the force with wrench

The torque required to open the jar remains the same.
Now, the radius (length of wrench) \(R = 14\space cm=0.14\space m\)
Using \(\tau = F\times R\), we can find \(F\).
\(F=\frac{\tau}{R}\)
Substitute \(\tau = 3\space N\cdot m\) and \(R = 0.14\space m\)
\(F=\frac{3}{0.14}\approx21.43\space N\)

Answer:

\(21.43\space N\)