A light, cubical container of volume a 3 is initially filled with a liquid of mass density ρ as shown in Figure P15.5la. The cube is initially supported by a light string to form a simple pendulum of length L i , measured from the center of mass of the filled container, where L i >> a . The liquid is allowed to flow from the bottom of the container at a constant rate ( dM/dt ). At any time t , the level of the liquid in the container is h and the length of the pendulum is L . (measured relative to the instantaneous center of mass) as shown in Figure P15.51b. (a) Find the period of the pendulum as a function of time. (b) What is the period of the pendulum after the liquid completely runs out of the container? Figure P15.51
A light, cubical container of volume a 3 is initially filled with a liquid of mass density ρ as shown in Figure P15.5la. The cube is initially supported by a light string to form a simple pendulum of length L i , measured from the center of mass of the filled container, where L i >> a . The liquid is allowed to flow from the bottom of the container at a constant rate ( dM/dt ). At any time t , the level of the liquid in the container is h and the length of the pendulum is L . (measured relative to the instantaneous center of mass) as shown in Figure P15.51b. (a) Find the period of the pendulum as a function of time. (b) What is the period of the pendulum after the liquid completely runs out of the container? Figure P15.51
Solution Summary: The author explains the period of the pendulum as a function of time.
A light, cubical container of volume a3 is initially filled with a liquid of mass density ρ as shown in Figure P15.5la. The cube is initially supported by a light string to form a simple pendulum of length Li, measured from the center of mass of the filled container, where Li>> a. The liquid is allowed to flow from the bottom of the container at a constant rate (dM/dt). At any time t, the level of the liquid in the container is h and the length of the pendulum is L. (measured relative to the instantaneous center of mass) as shown in Figure P15.51b. (a) Find the period of the pendulum as a function of time. (b) What is the period of the pendulum after the liquid completely runs out of the container?
A section of uniform pipe is bent into an upright U shape and partially filled with water, which can then oscillate back and forth in simple harmonic motion. The inner radius of the pipe is r = 0.024 m. The radius of curvature of the curved part of the U is R = 0.23 m. When the water is not oscillating, the depth of the water in the straight sections is d = 0.37 m.
Enter an expression for the mass of water in the tube, in terms of the defined quantities and the density of water, ρ. Use the approximation r << R.
Calculate the mass of the water, in kilograms. Take ρ = 1000 kg/m3.
Enter an expression for the force constant of the U-shaped column of water when displaced from equilibrium, in terms of the defined quantities, ρ, and g. This constant is analogous to the spring constant in Hooke’s law.
Find the value of the force constant, in newtons per meter. Take ρ = 1000 kg/m3 and g = 9.81 m/s2.
Calculate the period of oscillation, in seconds.
A large rectangular cube made of wood has the follow dimentions: a height, h = 2m, and an area od A = 0.25m^2. The wood that the cube is made of has a density of 800kg/m^3. The cube is then place vertically in water where it floats to rest. The density of the water is 1000kg/m^3. Then the cube is pushed down slightly (by a distance y) and released. The resulting motion is simple harmonic motion.
A) Determine the mass of the cube.
B) Determine the depth,d, that the cube will float.
C) If the cube is pushed further down under water by a distance, y, write an expression for the net force on the block in terms of: y,A,g,p. Where g=9.8m/s^2
D)Use the expression for the net forcee found in part C), and apply newton's second law (Fnet = ma) to the situation of the cube that is being pushed down slightly to derive an equation for the vertical accerlation (ay) (hint: dont forget to pick a positive direction)
Compare your results from part D) to the equation for simple harmonic motion using…
A solid ball 300 cm in diameter is submerged in a lake of such depth that pressure exerted by water is 9.8x10^4 N/m^2. Find the change in volume of the ball at this depth. Bulk of the modulus of the material of the ball is 10^12 N/m^2. [1.386 c.c.]
Chapter 15 Solutions
Physics for Scientists and Engineers, Technology Update, Hybrid Edition (with Enhanced WebAssign Multi-Term LOE Printed Access Card for Physics)
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