lab assignment 4 - PHYS133

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Dec 6, 2023

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Mariah Keller Castillo 5786597 PHYS133 K002

PRE-LAB QUESTIONS 1. Draw a free body diagram of a hanging mass before it is submerged in water. Make sure to label your forces. 2. Draw a free body diagram of a hanging mass after it is submerged in water. Make sure to label your forces. Which force is the force you measure with the spring scale?

3. Apply Newton’s second law to your free body diagram in Pre-Lab Question 2 to solve for the magnitude of the buoyant force. EXPERIMENT 1: BUOYANT FORCE AND FLOATING Data Sheet Table 1. Number of Washers a Clay Boat Can Hold Before Sinking Type of Liquid Number of Washers Plain Water 1 Salt Water 3 Post-Lab Questions 1. What did you observe when you placed the ball of clay into the beaker?

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I observed that the clay ball sinks. I would assume that this happens because the clay ball is denser than water. The density of an object is determined by comparing its mass to its volume. If an object is denser than the fluid it's placed in, it will sink. 2. What were characteristics of the boat design that floated the best? Explain why this works, and the clay ball fails to float using Archimedes’ Principle. The boat design that floated the best had the following characteristics: Wide and Flat Bottom: The boat's hull was wide and flat, allowing it to displace a significant amount of water. The wider the hull, the more water it can displace, resulting in a greater buoyant force. Low Center of Gravity: The boat's design had a low center of gravity, which made it stable and less prone to tipping over. A low center of gravity helps maintain equilibrium, ensuring the boat doesn't capsize. Symmetrical Shape: The boat was symmetrical, ensuring even weight distribution. Symmetry can make the boat more stable and balanced. Adequate Volume: The boat had enough volume to displace an amount of water equal to or greater than its own weight. These characteristics work because of Archimedes' Principle. Archimedes' Principle states that any object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. In the case of a well-designed boat: The wide and flat bottom allows the boat to displace a larger volume of water, which generates a greater buoyant force. A low center of gravity ensures that the boat doesn't tip over easily, maintaining its equilibrium. Symmetry contributes to the boat's stability by ensuring even weight distribution. The clay ball, on the other hand, fails to float because it is denser than the water. Its weight exceeds the buoyant force acting on it. Archimedes' Principle tells us that for an object to float, it must displace an amount of water with a weight equal to or greater than the weight of the object. The clay ball's density is such that it displaces an insufficient volume of water to generate a buoyant force greater than its own weight, causing it to sink .

3. How much water does an object have to displace before it will float? An object will float when it displaces an amount of water (or any fluid) equal to or greater than its own weight. This is a fundamental concept based on Archimedes' Principle, which states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In practical terms, this means that if the weight of the water (or fluid) displaced by the object is less than the weight of the object itself, the object will sink. If the weight of the water displaced is equal to or greater than the weight of the object, the object will float. So, for an object to float, it must displace enough water to generate a buoyant force that balances or exceeds its own weight. This concept is critical in understanding the buoyancy of objects in fluids, such as ships and boats floating on water. 4. If your clay boat weighs .005 kg and is floating, what is the upward force the water is exerting on the boat? Gravity: Gravity is a fundamental force that pulls objects towards the Earth. The weight of the clay boat is calculated as: Weight (W) = mass (m) × acceleration due to gravity (g) For the clay boat with a mass of 0.005 kg: W = 0.005 kg × 9.8 m/s² ≈ 0.049 N Therefore, the weight of the clay boat is approximately 0.049 Newtons (N). Buoyancy: Buoyancy is the upward force exerted by a fluid on a submerged object. When the clay boat is floating in water, the upward force (F) the water exerts on it is equal to the boat's weight, as described by Archimedes' Principle. F = Weight of the clay boat = 0.049 N The upward force exerted by the water is indeed 0.049 N.

5. How could you improve your boat design to increase the buoyant force without using more clay? Widening the boat or creating a boat with thinner clay walls could result in a greater displacement of water, and increased buoyancy. 6. In the second part of the experiment, does the boat hold more weight in the regular water or the salt mixture? What does this say about the relative densities of salt water and plain water? The boat will hold more weight in salt water because the density of salt water is more than density of regular water . The density of salt water is 1.029g / cm3 .

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