: Object performing SHM with mass of 0.5 k.g force constant 10 N/m and amplitude 3 cm. (a) What is the total energy of object (b) What is its maximum speed? (c) What is the speed at x = 2 cm ? (d) What are kinetic and potential energies when x = 2 cm ?
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- Grandfather clocks keep time by advancing the hands a set amount per oscillation of the pendulum. Therefore, the pendulum needs to have a very accurate period for the clock to keep time accurately. As a fine adjustment of the pendulum’s period, many grandfather clocks have an adjustment nut on a bolt at the bottom of the pendulum disk. Screwing this nut inward or outward changes the mass distribution of the pendulum by moving the pendulum disk closer to or farther from the axis of rotation at O. Let mp = 0.7 kg and r = 0.1 m Model the pendulum as a uniform disk of radius r and mass mp at the end of a rod of negligible mass and length L – r, and assume that the oscillations of θ are small. If the pendulum disk is initially at a distance L = 0.85 m from the pin at O, how much would the period of the pendulum change if the adjustment nut with a lead of 0.5 mm was rotated four complete rotations closer to the disk? In addition, how much time would the clock gain or lose in a 24 h…A 5.0 kg weight is hanging from an ideal spring with a k of 250N/m. It is pulled .15m from equalibrium. Find it's maximum displacement the elastic potential energy of spring just as the block is being released the maximum speed the block will have during its motion the displacement of the block from equilibrium when the kinetic energy of the block is equal to the elastic potential energy of the spring The block is then brought to rest at equilibrium. The block is then pulled down half the original distance. Will the new period for the motion of the block be greater than, less than, or equal to the original period for the motion of the block? Why? The first block is brought to rest at equilibrium again. An identical block is launched up into the first block. The new block is moving with an initial speed of v=5.0m/s when it collides with and sticks to the original block. Calculate the maximum compression of the spring after the collision of the two blocks.Problem 2 ( ). A very light spring with spring constant 200 N/m hangs vertically the ceiling with equilbrium length Lo = 6 cm. When a 300 g mass is attached to the end spring, the mass-spring system extends to a new equilibrium length. Lo y = 0 (a) What is the length L of the spring when the mass-spring system is in equilibrium? If the mass is released from rest with the spring at its original equilibrium length (b) 6 cm, find the velocity of the mass when the spring has stretched to the length L you found in (a). 000000
- A pendulum of mass 90 gm and length 60 cm is left to swing from an initial angle of 40 degrees, and seen to raise up to an angle of 38 degrees when it reaches the other side. How much energy did the pendulum lose? Why is there a loss of energy?Using the spring force, F = -kx, calculate: a) The work done by an external force stretching the spring a distance L away from the equilibrium length. b) At a stretch length L, how much potential energy is stored in the spring? If a mass m is attached to the spring and released from a stretch length L, what is the maximum velocity c) of the mass? d) At what x coordinate does this maximum velocity occur?The potential energy of an object attached to a spring is 2.40 J at a location where the kinetic energy is 1.70 J. If the amplitude A of the simple harmonic motion is 20.0 cm, calculate the spring constant k and the magnitude of the largest force Fspring, max that the object experiences.