572 mm
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Q: x = 5.00 cos (5t + = where x is in centimeters and t is in seconds. (a) At t = 0, find the position…
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Q: MY NOTES PRACTICE ANOTHER In an engine, a piston oscillates with simple harmonic motion so that its…
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A: The equation for the piston's position is given by x = 8.00 cos (3t+π/6)
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The period of vibration for a barrel floating in salt water is found to be 0.58 s when the barrel is empty and 1.8 s when it is filled with 55 gallons of crude oil. Knowing that the density of the oil is 900 kg/m 3, determine (a) the mass of the empty barrel, (b) the density of the salt water, psw {Hint: The force of the water on the bottom of the barrel can be modeled as a spring with constant k=pswgA.}
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- In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 3.00 cos(4t +(pi/6)) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston.(b) At t = 0, find velocity of the piston.(c) At t = 0, find acceleration of the piston. (d) Find the period and amplitude of the motion.1) A ball of mass, m = 2.50 kg, floats on a pool of fluid, L-1.00 m wide. It is attached to supports at either end of the pool by springs, as shown in Fig.-1. The left spring has a spring constant, A = 65.0 N/m, and equilibrium length, L1-0.600 m. The spring on the right has a spring constant, k2-75.0N/m, and equilibrium length, L20.800m L = 1.00 m ki, Li Figure 1 -A ball of mass, m = 2.50 kg, floats on a pool of fluid, L = 1.00 m wide. It is attached to supports at either end of the pool by springs. The left spring has a spring constant, A = 65.0 N/m, and equilibrium length, L1 = 0.600 m. The right spring has a spring constant. ka = 75.0 N/m, and equilibrium length, L2 = 0.800 m. (Not to scale.) a) The ball is initially at rest at position, x - d. It's then pulled to the center between the two supports at 0.500 m, and let go. How long after it's let go does it take to return to x- d? (Neglect the drag of the fluid.) Supposing we now consider that the fuld exerts a drag force on the…In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 5.00 cos5t + (5t + 7 ) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. cm (b) At t = 0, find velocity of the piston. cm/s (c) At t= 0, find acceleration of the piston. cm/s² (d) Find the period and amplitude of the motion. period S amplitude cm
- A steel bar 100 mm long and having a square cross section 20 mm on an edge is pulled in tension with a load of 89 KN and experiences an elongation of 0.10 mm. Assuming that the deformation is entirely elastic, calculate the elastic modulus of the steel.A light balloon filled with helium of density 0.179 kg/m³ is tied to a light string of length L = 5.45 m. The string is tied to the ground, forming an "inverted" simple pendulum (shown in (a) of following figure). Air a 100->> L He Air L He i Determine the period of the motion (in s). Take the density of air to be 1.18 kg/m³. (Hint: Use an analogy with the simple pendulum. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.)In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 5.00 cos (4t+ (4t + 1/7) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. cm (b) At t = 0, find velocity of the piston. cm/s (c) At t = 0, find acceleration of the piston. cm/s² (d) Find the period and amplitude of the motion. period amplitude S cm
- Chapter 37, Problem 012 The length of a spaceship is measured to be exactly 1/2 its rest length. (a) What is the speed parameter ß of the spaceship relative to the observer's frame? (b) By what integer factor do the spaceship's clocks run slow, compared to clocks in the observer's frame? (a) Number Units (b) Number UnitsIn a standard tensile strain test, a 20 mm diameter aluminum rod is subjected to a tensile force of P = 30KN. If μ = 0.35 (Poisson's ratio) and E = 70 GPa (Young's modulus), determine: a) The elongation of the rod in a calibrated length of 150 mm and b) The change in the diameter of the rodBy what percentage does the density of water increase at a depth of 1.25 km below the surface? Bulk modulus of water is 220 * 10 ^ 9 Pa. Density of water is 100 * 10 ^ 3 * ka / (m ^ 3)
- Find the minimum diameter of a (50 m)-long nylon string that will stretch no more than (1 cm) when a load of (70 kg) is suspended from its lower end. Assume that the Young modulus equals to 3.51*10 N/m? 3.35 cm 3.53 cm 35.3 cm 33.5 cmThe face of an aluminum plate, which is fixed in place, measures 90 cm by 90 cm. The thickness of the plate is 6 cm. A force parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 10^10 Pa. Find the displacement of the upper force.In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 8.00 cos (5t + TC where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. cm (b) At t = 0, find velocity of the piston. cm/s (c) At t = 0, find acceleration of the piston. cm/s² (d) Find the period and amplitude of the motion. period S amplitude cm