Question

of basket a?
figure 10 shows a pulley system with two baskets. the radii of the pulley parts are 4.5 cm and 1.1 cm. the basket on the right has a mass of 0.23 kg. what is the mass of basket a? (assume the pulley is massless and frictionless.)

Explanation:

This is a problem about the principle of levers (torque balance), where the torque on both sides of the lever should be equal. Torque \( \tau = r \times F \), and in the case of weight, \( F = mg \), so the torque balance equation is \( r_1 \times m_1 \times g=r_2 \times m_2 \times g \), and \( g \) can be canceled out, getting \( r_1 \times m_1 = r_2 \times m_2 \). We need to find the mass \( m_A \) of basket A.

Step 1: Identify the radii and the known mass

Let the radius corresponding to basket A be \( r_A = 4.5\space cm \), the radius corresponding to the known - mass basket be \( r = 1.1\space cm \), and the mass of the known - mass basket \( m = 0.23\space kg \).
According to the torque - balance principle \( r_A\times m_A=r\times m \)

Step 2: Solve for \( m_A \)

We can re - arrange the formula \( m_A=\frac{r\times m}{r_A} \)
Substitute \( r = 1.1\space cm \), \( m = 0.23\space kg \) and \( r_A = 4.5\space cm \) into the formula:
\( m_A=\frac{1.1\times0.23}{4.5}=\frac{0.253}{4.5}\approx0.056\space kg \) (rounded to three decimal places)

Answer:

The mass of basket A is approximately \( 0.056\space kg \)