Energy Energy vs. position t = 1.940 s 8 4 N 0 >x (m) 20 40 60 80 100 120 140 160 180 200 Height (cm) 40 T 20 - Length (cm) 20 40 60 80 100 120 140 160 180 200 Play Pause > Reset g = 10m/s^2 In our example, the ramp has the shape of a 3-4-5 triangle (the 3 side is vertical and the 4 side is horizontal). The block, which has a mass of 2.00 kg, is released from rest from the top of the frictionless incline. It slides a distance of 2.50 m down the ramp before contacting the spring (dropping in height by 1.50 m before reaching the spring). Then, the block compresses the spring by 2.50 m before coming to rest for an instant. Determine the spring constant. N/m Continuing from part (a), by how much is the spring compressed when the block reaches its maximum speed? Continuing from the previous parts, determine the maximum speed reached by the block. m/s Energy vs. position E 0.5 E -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 08 1 x (m) The graph above shows the elastic potential energy (blue), kinetic energy (red), and total energy (green), all as a function of position, for a ball oscillating on a spring. The equilibrium position of the ball is x = 0 m. The value of the maximum energy is E = 12.0 J, and the period of oscillation is T = 2.00 s. We will neglect resistive forces. Determine the value of the spring constant of the spring. N/m The value of the maximum energy is E = 12.0 J, and the period of oscillation is T = 2.00 s. We will neglect resistive forces. Determine the mass of the ball. kgA flexible tube can be used as a simple siphon to transfer fluid from one container to a lower container. See the dimensions given in the figure, take atmospheric pressure to be 101.3 kPa, and use 9 = 9.80 N/kg. Neglect viscosity, and assume the tube has a fixed cross-sectional area. 20 cm 10 ch 60 cm Note that you will most likely get different numbers forthe different parts below. As usual, 3 good way to handle that is to solve the problem using variables, and only plug in numbers at the end. The fluid has a density of 880 kg/m3, and the tube has a cross- sectional area that is much smaller than the cross-sectional area of the higher container. Calculate the speed at which the fluid flows out of the tube at point Z. m/s The fluid has a density of 880 kg/m3, and the tube has a cross- sectional area that is much smaller than the cross-sectional area of the higher container. Calculate the speed at which the fluid is flowing through the tube at point Y. m/s The fluid has a density of 880 kg/m3, and the tube has a cross- sectional area that is much smaller than the cross-sectional area of the higher container. Calculate the absolute pressu re inside the tube at point Y. kPa A wooden ball with a weight of 16.0 N hangs from a string tied to a spring scale. When the ball is at rest, exactly 50% submerged in water, the spring scale reads 4.00 N. For this problem, we will use a density of water of 1000 kg/m3, and we will use g = 10.0 m/sz. Ifthe ball was only 40.0% submerged in water instead, what would the spring scale read? N A wooden ball with a weight of 16.0 N hangs from a string tied to a spring scale. When the ball is at rest, exactly 50% submerged in water, the spring scale reads 4.00 N. For this problem, we will use a density of water of 1000 kg/m3, and we will use g = 10.0 m/sz. Determine the density ofthe ball. _ kg/m3 A wooden ball with a weight of 16.0 N hangs from a string tied to a spring scale. When the ball is at rest, exactly 50% submerged in water, the spring scale reads 4.00 N. For this problem, we will use a density of water of 1000 kg/m3, and we will use g = 10.0 m/sz. Determine the volume of the ball. The fluid in the U is water, and there is a 10.0 cm difference between the water levels on the two sides. Determine the magnitude ofthe pressure difference between points 1 and 2 in the Venturi tube. Pa The Venturi tube has air flowing through it. Ifthe cross-sectional area ofthe Venturi tube is 5 times larger at point 1 than it is at point 2, what is the airspeed at point 2? mls Wenturi tube is a tube with a constriction in it. Pressure n a Venturi tube can be measured by attaching a U ;haped fluid-lled device to the Venturi tube as shown in .he figure above. The density of air is 1.20 kg/m3 and the tensity of water is 1000 kg/m3. Use 3 = 10.0 m/s2. A cube ofwood,10 cm on a side, is placed in a container ofwater. The cube floats with exactly 42% of its volume submerged. The density of water is 1000 kg/m'. The density of oil is 800 kgfrn'. Now. the cube is tied to the bottom of a container that's filled with water and oil, as shown in the diagram. The string's length is such that the cube is exactly 50% in the oil and 50% in the water. Determine the tension in the string. A cube ofwood, 10 cm on a side, is placed in a container ofwater. N The cube oats with exactly 42% of its volume submerged. The density of water is 1000 kg/m3. The cube is then placed into a container ofoil. The oil has a density of 800 kg/m3. What percentage of the cube is submerged now? % water