Astronauts use a uniform rod with a mass of 10.6 kg and a length of 2 meters to determine the acceleration due to gravity on Planet Todd? To do this, they attach the rod to a pivot point that is 0.3 meters from one end of the rod and then allow the rod to hang vertically. From its equilibrium position, the rod is displaced 7.9 degrees and released. The time for 5 oscillations is found to be 15.5 seconds. What is the acceleration due to gravity on the planet?
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- A tall building is swaying back and forth on a gusty day. The wind picks up and doubles the amplitude of the oscillation.By what factor does the maximum speed of the top of the building increase?By what factor does the maximum acceleration of the top of the building increase?A peg on a turntable moves with a constant tangential speed of 0.67 m/s in a circle of radius 0.26m. The peg casts a shadow on a wall. Find the following quantities related to the motion of the shadow.1) Find the period. Express your answer using two significant figures. T=(?)s2) Find the amplitude. A=(?)m3) Find the Max Speed Vmax= (?) m/s4) Find the maximum magnitude of the acceleration. aMax=(?)m/s^2A spider can tell when its web has captured, say, a fly because the fly's thrashing causes the web threads to oscillate. A spider can even determine the size of the fly by the frequency of the oscillations. Assume that a fly oscillates on the capture thread on which it is caught like a block on a spring. What is the ratio of oscillation frequency for a fly with mass m to a fly with mass 2.5m?
- A boy of mass 49.8 kg standing on the end of a diving board depresses it vertically downward a distance of 15.7 cm. By pushing down on the board with a force a little greater than his weight, the boy can depress the end of the board a bit farther. The boy and the board then oscillate up and down. Estimate the period of oscillation, assuming that the force the board exerts is approximately like that of a compressed spring, in other words, that it obeys Hooke's law.The balance wheel of a watch oscillates with angular amplitude 1.0n rad and period 0.34 s. Find (a) the maximum angular speed of the wheel, (b) the angular speed of the wheel at displacement 1.0n/2 rad, and (c) the magnitude of the angular acceleration at displacement 1.0n/4 rad. (a) Number Units (b) Number Units (c) Number UnitsYou have made a physical pendulum by swinging a rod of mass M = 1.08 kg and length L = 1.45 meters around its end. The mass of the rod is distributed uniformly along its length. We will assume that the amplitude of the swing is max = 19.34 degrees. Solid Rod Swings in Simple Harmonic Motion ^ 0=-0, max 0=+0₁ max Determine all the following: The FORMULA for the moment of inertia of your rod, I = The distance from the pivot point to the Center-Of-Mass, d = The angular frequency of the pendulum, w = The amplitude of the motion in radians, max = radians The angular velocity when 0 = 64% of full swing, w(0 = 0.64 0max): NOTE: The first question requires a FORMULA, not a value. rad/sec = meters rad/sec
- An object oscillates with an angular frequency ω = 6 rad/s. At t = 0, the object is at x0 = 1.5 cm. It is moving with velocity vx0 = 14 cm/s in the positive x-direction. The position of the object can be described through the equation x(t) = A cos(ωt + φ). What is the the phase constant φ of the oscillation in radians? Write an equation for the amplitude A of the oscillation in terms of x0 and φ. Use the phase shift as a system parameter. Calculate the value of the amplitude A of the oscillation in cm.An object hanging from a vertical spring oscillates with a period of 0.35 s. Suppose the same object and spring are placed on a horizontal frictionless surface and the object is in a horizontal circle swung (uniform circular motion) with the open end of the spring as the pivot. How many rotations per minute is needed to stretch the spring by 15%?A uniform stick of length L and mass m is pivoted at one of its ends. Derive an equation for the period of oscillation when the stick is set into small oscillation. Answer in terms of m, g, and L as needed.
- A thin uniform rod (mass = 0.24 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.1 s and an angular amplitude of 9.6°. (a) What is the length of the rod? (a) What is the maximum kinetic energy of the rod as it swings?We can model the motion of a bumblebee’s wing as simple harmonic motion. A bee beats its wings 250 times per second, and the wing tip moves at a maximum speed of 2.5 m/s. What is the amplitude of the wing tip’s motion?There are more than 300 species of hummingbirds in the world and about 10 species regularly breed in the United States. One of which is the Ruby-throated Hmmingbird who can flap its wings with an angular speed of 332 rad/s. Calculate the period of its flapping motion.