This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Here is the solution for Item 3: Item 3 a) To determine the mass of Jamal's bottle using the available materials, you would set up a simple lever system based on the principle of moments. Step 1: Balance the metre rule on the knife edge at its center of gravity (typically the 50 cm mark) to ensure it is horizontally level. Step 2: Suspend the known 100g mass from one side of the metre rule using one piece of thread. Step 3: Suspend Jamal's bottle from the other side of the metre rule using the second piece of thread. Step 4: Adjust the positions of both the 100g mass and the bottle along the metre rule until the rule balances horizontally on the knife edge. Step 5: Measure the distance from the knife edge to the point where the 100g mass is suspended (d_1) and the distance from the knife edge to the point where the bottle is suspended (d_2). Step 6: Apply the principle of moments: The clockwise moment must equal the anticlockwise moment. m_1 d_1 = m_2 d_2 where m_1 is the known mass (100g), d_1 is its distance from the pivot, m_2 is the unknown mass of the bottle, and d_2 is its distance from the pivot. You can then calculate m_2. Use a balanced metre rule as a lever, suspending the 100g mass and the bottle on opposite sides. Adjust positions until balanced, measure distances, and apply the principle of moments to find the bottle's mass. b) Step 1: State the principle of moments. The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments about a pivot must equal the sum of the anticlockwise moments about the same pivot. Clockwise Moment = Anticlockwise Moment m_1 d_1 = m_2 d_2 Here, m_1 is the known mass, d_1 is its distance from the knife edge, m_2 is the mass of the bottle, and d_2 is its distance from the knife edge. Step 2: Substitute the given values into the equation. Given: m_1 = 100 g d_1 = 15.0 cm d_2 = 37.5 cm (100 g) × (15.0 cm) = m_2 × (37.5 cm) Step 3: Solve for the mass of the bottle (m_2). 1500 g · cm = m_2 × (37.5 cm) m_2 = 1500 g · cm37.5 cm m_2 = 40 g Step 4: Determine if the bottle qualifies for sale. The entrepreneur buys bottles that weigh more than 30g. Since m_2 = 40 g, and 40 g > 30 g, Jamal's bottle qualifies for sale. The mass of Jamal's bottle is 40 g. Yes, the bottle qualifies for sale because 40 g > 30 g. What's next?