Physics Answer Note #18

Question 1 What are the conditions that must be satisfied for total internal reflection to occur? Answer Total internal reflection is a phenomenon that occurs when a ray of light passing through a medium reaches the boundary with another medium and is completely reflected back into the same medium, with no light being transmitted into the second medium. This phenomenon only occurs when certain conditions are met. One of the conditions for total internal reflection to occur is that the incoming ray of light must be travelling from a medium with a higher index of refraction to a medium with a lower index of refraction. This can be represented mathematically through Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media involved. When this ratio is greater than 1, total internal reflection can occur. Another condition that must be satisfied for total internal reflection to occur is that the angle of incidence must be greater than the critical angle. The critical angle is the angle of incidence at which the angle of refraction is 90 degrees, meaning that the refracted ray is parallel to the boundary between the two media. This critical angle can be calculated using the equation c = sin^-1(n2/n1), where n1 is the index of refraction of the first medium, and n2 is the index of refraction of the second medium. Furthermore, the interface between the two media must be smooth and clean for total internal reflection to occur. Any irregularities or impurities on the boundary can result in some light being transmitted into the second medium. Question 2 Calculate the average horsepower required to raise a 150kg to a height of 20m in a time of 1 minute. Answer In order to accurately determine the average horsepower required for this task, we must first understand the concept of power and how it relates to lifting a mass to a certain height in a given time frame. Power is defined as the rate at which work is done, or the amount of energy transferred per unit of time. The unit of measurement for power is watts (W) or horsepower (hp). To begin, we must first convert the mass of the object from kilograms (kg) to pounds (lbs) because horsepower is commonly measured in pounds and distance is measured in feet. Therefore, 150kg is equal to 330 lbs. Next, we need to determine the work done in lifting the object to a height of 20m. Work is defined as the transfer of energy to an object by applying a force over a displacement, and is calculated by the equation W=mgΔh where m is the mass of the object, g is the acceleration due to gravity (9.8m/s^2), and Δh is the change in height. Using the values given in the question, we can calculate the work done as W=(330 lbs)(9.8m/s^2)(20m) = 64,680 lb-ft. To convert this to horsepower, we must divide by the time it took to complete the task, which in this case is 1 minute or 60 seconds. Therefore, the power required to lift a 150kg object to a height of 20m in 1 minute is (64,680 lb-ft) / (60 s) = 1,078 hp. Question 3 A 2.0cm×2.0cm×7.0cm block floats in water with its long axis vertical. The length of the block above water is 1.0 cm . What is the block's mass density? Answer According to the given information, we can determine the block's density by using the formula density = mass/volume. In this case, the volume of the block is 2.0cm x 2.0cm x 7.0cm = 28.0 cm^3. Since the length of the block above water is 1.0cm, the volume above water is 2.0cm x 2.0cm x 1.0cm = 4.0 cm^3. To find the volume of the block underwater, we simply subtract the volume above water from the total volume: 28.0 cm^3 - 4.0 cm^3 = 24.0 cm^3. Now, we need to find the mass of the block. Since it is floating in water, the force exerted on the block by water is equal to the weight of the block. According to Archimedes' principle, the buoyant force acting on the block is equal to the weight of the water displaced by the block. Therefore, the weight of the block is equal to the weight of the water it displaces. The weight of the water displaced by the block can be calculated using the formula weight = density x volume x acceleration due to gravity. The density of water is 1.0 g/cm^3, and the volume of the water displaced is 24.0 cm^3. The acceleration due to gravity is approximately 9.8 m/s^2. Thus, the weight of the water displaced by the block is equal to (1.0 g/cm^3) x (24.0 cm^3) x (9.8 m/s^2) = 235.2 g. Since the weight of the block is equal to the weight of the water displaced, we can conclude that the mass of the block is also 235.2 g. Finally, we can calculate the density of the block using the formula density = mass/volume. Therefore, the density of the block is 235.2 g/28.0 cm^3 = 8.4 g/cm^3. In short, the mass density of the 2.0cm x 2.0cm x 7.0cm block is 8.4 g/cm^3. This calculation was done using the concept of buoyancy and the formula for density. Question 4 A ball is dropped from a 1.5m above a tile floor and rebounds to a height of 1m. Find the coefficient of restitution between the ball and the floor. Give the correct solution of the given answer is 0.82m/s Answer The coefficient of restitution (COR) is a measure of the elasticity of a collision between two objects. In this case, it represents the ratio of the final velocity of the ball after the collision to its initial velocity. In simpler terms, it measures how much energy is lost or retained during the collision. To calculate the COR, we need to use the formula COR = (vf/vi), where vf is the final velocity and vi is the initial velocity. In this scenario, we are given the initial height (1.5m) and final height (1m) of the ball, but we do not know the initial velocity. Therefore, we need to find it using the conservation of energy principle. According to the conservation of energy, the total energy of a closed system remains constant. In this case, the closed system is the ball and the Earth. Therefore, the initial potential energy of the ball at 1.5m height will be converted into its final kinetic energy at 1m height. Using the equation for potential energy (PE=mgh) and kinetic energy (KE=1/2mv^2), we can equate the initial potential energy to the final kinetic energy. PE = KE mgh = 1/2mv^2 mg(1.5) = 1/2mv^2 v = √(2gh) Substituting the values of g (9.8m/s^2) and h (1.5m), we get: v = √(2x9.8x1.5) = 5.42m/s Now that we have the initial velocity, we can calculate the COR using the formula mentioned earlier. COR = (vf/vi) = (1/5.42) = 0.185 or 18.5% Therefore, the coefficient of restitution between the ball and the floor is 0.185 or 18.5%. Question 5 given the answer for part A is 2.5 calculate the rest:For the capacitor network shown in (Figure 1), the potential difference across ab is 38 V, capacitors are parallel Find the total charge stored in this network.Find the charge on the 150 nF capacitor. Express your answer in microcoulombs to one decimal place.Find the total energy stored in the network. C1= 150nF and C2 = 120 nF V(ab)=38 V, the capacitors are parallelo find the total charge stored in the network, you can use the formula Q = C * V, where Q is the charge, C is the capacitance, and V is the voltage. 2. Calculate the total charge by summing the charges stored in each capacitor in the network. 3. To find the charge on the 150nF capacitor, use the same formula Q = C * V with the capacitance of the 150nF capacitor and the given potential difference. 4. Convert the charge to microcoulombs by dividing by 1,000. 5. To find the total energy stored in the network, use the formula E = 0.5 * C * V^2 for each capacitor and sum the energies for all capacitors in the network. Answer To calculate the total charge stored in the network, we can use the formula Q = C * V, where Q is the charge, C is the capacitance, and V is the voltage. In this case, we have V = 38 V and C = C1 + C2 = 150 nF + 120 nF = 270 nF. Therefore, the total charge stored in the network is Q = (270×10^-9 F) * (38 V) = 10.26*10^-6 C = 10.3 μC to one decimal place. To find the charge on the 150 nF capacitor, we can use the same formula as above, but this time we only need to consider the capacitance of the 150 nF capacitor. Thus, Q = (150×10^-9 F) * (38 V) = 5.7*10^-6 C = 5.7 μC. To convert the charge to microcoulombs, we divide by 1,000. Therefore, the charge on the 150 nF capacitor is 5.7 μC. Next, we can find the total energy stored in the network by using the formula E = 0.5 * C * V^2 for each capacitor and summing the energies for all capacitors in the network. Thus, E = 0.5 * [(150 nF) * (38 V)^2 + (120 nF) * (38 V)^2] = 130.5 mJ.