A block is in SHM on the end of a spring, with position given by x = xmcos(ω t + φ). If φ = 0.428 rad, then at t = 0 what percentage of the total mechanical energy is potential energy?
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- 5. 0 m feeeee A mass m = 25 kg is sitting on a slope with = 20°. There is no friction between the mass and the slope. The mass is attached to a spring with rest length lo = 5 cm that is mounted at the top of the slope. When the mass is released, the spring stretches an amount Ax = 6.2 cm (as measured along the slope, total length is now 11.2 cm) when the system reaches static equilibrium. a.) Draw the free-body diagram of the mass, showing all forces acting on the mass. b.) Calculate the value of the spring constant, k.An ideal spring hangs from the ceiling. A 2.15 kg mass is hung from the spring, stretching the spring a distance d = 0.0835 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L = 0.0255 m from the equilibrium position and released. What is the kinetic energy K of the mass at the instant it passes back through the equilibrium position? K = J d Equilibrium position www. 14 L CoA spring AB of natural length 0.5 m and modulus of elasticity 25 N is fixed at A. The other end is joined to another spring BC of natural length 0.8 m and modulus of elasticity 40 N. A weight WN is attached at C and the system hangs vertically in equilibrium so that AC=2m. (i) Find the extension of the two springs. (ii) Find W. Answer: (i) (ii) 0.35 m, 0.35m 17.5 N
- The springs of a pickup truck act like a single spring with a force constant of 1.9×105 N/m1.9×105 N/m. By how much will the truck be depressed by its maximum load of 550 kg?distance = cm If the pickup truck has four identical springs, what is the force constant of each?k=k= N/mA spring 1.50 m long with force constant 471 N/m is hung from the ceiling of an elevator, and a block of mass 14.1 kg is attached to the bottom of the spring. (a) By how much is the spring stretched when the block is slowly lowered to its equilibrium point? (Enter the magnitude only.) 0.29 m (b) If the elevator subsequently accelerates upward at 1.84 m/s2, what is the position of the block, taking the equilibrium position found in part (a) as y = 0 and upwards as the positive y-direction. (Indicate the direction with the sign of your answer.) 0.054 X Your response differs from the correct answer by more than 10%. Double check your calculations. m (c) If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion? 0.35 mProblem 9: An ideal pendulum of length L=1.1 m supports a mass of m =0.5 kg. Initially the pendulum is lifted such that it makes an angle of 0 = 26 degrees with respect to the vertical. m 10
- A 0.050 kg object is attached to a spring with a spring constant of 150.0 N/m. The other end of the spring is attached to a wall in such a way that it rests on a frictionless horizontal surface. A force is exerted on the spring so that it experiences simple harmonic motion. How much work would be done on this spring to compress it by 15.0 cm?A spring lies on a horizontal table, and the left end of the spring is attached to a wall. The other end is connected to a box. The box is pulled to the right, stretching the spring. Static friction exists between the box and the table, so when the spring is stretched only by a small amount and the box is released, the box does not move. The mass of the box is 0.75 kg, and the spring has a spring constant of 77 N/m. The coefficient of static friction between the box and the table on which it rests is us = 0.59. How far can the spring be stretched from its unstrained position without the box moving when it is released?An m = 20.0 g object is held against the free end of a d, spring of constant k = 25.0 N/m that is compressed a LO000 distance x = 10.0 cm from its equilibrium length. Once released, the object slides d1 = 1.15 m across the tabletop and eventually lands dɔ = 1.03 m from the edge of the table on the floor, as shown in the figure. Calculate the coefficient of friction µ between the table and the object. The sliding distance includes the compression of the spring, and the tabletop is h = 1.00 m above the floor level. d,
- A 50 cm long spring with spring constant 302 N/m has a mass 1.4 kg attached to it, and it can ocillate on a horizontal table without any friction. When the spring is pulled so that its length is 59 cm, what is the magnitude of the restoring force exerted by the spring?A 2 kg mass attached to a horizontal ideal spring with spring constant k = 8 n2 N/m oscillates in SHM. a) Att = 0, the mass is at x = +0.5 m from its equilibrium position and has a velocity of- 3.0 m/s. Calculate K and U at t = 0 and then find E = K +U, the total mechanical energy of the system. b) From your answer in a), find A, the amplitude of the oscillations c) Find o, the angular frequency. d) Find o, the phase angle in radians from initial conditions by evaluating: x (t) = A cos (@t + 4) and v(t) if x(0) = + 0.5 m and v(0) = - 3 m/s. %3D %3D | %3D %3DAn ideal spring hangs from the ceiling. A 1.65 kg1.65 kg mass is hung from the spring, stretching the spring a distance ?=0.0925 md=0.0925 m from its original length when it reaches equilibrium. The mass is then lifted up a distance ?=0.0315 mL=0.0315 m from the equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through the equilibrium position?