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1. [-15 Points] DETAILS SERPSE10 12.3.OP.005. MY NOTES PRACTICE ANOTHER = A mobile is constructed of light rods, light strings, and beach souvenirs as shown in the figure below. If m4 = 12.0 g, find values in g) for the following. (Let du = 4.20 cm, d2 = 5.20 cm, dz = 2.40 cm, d4 = 5.80 cm, d5 = 3.70 cm, and do = 4.50 cm.) d d2 d3 d4 d5 do mg m, ma mi (a) m1 = g (b) m2 = g (c) m3 = g (d) What If? If my accidentally falls off and shatters when it strikes the floor, the rod holding me will move to a vertical orientation so that m4 hangs directly below the end of the rod supporting m2. To what values should m2 and m, be adjusted so that the other two rods will remain in equilibrium and be oriented horizontally? (Enter your answers in g.) = m2 g m3 = g . 2. [-12 Points] DETAILS SERPSE10 12.3.P.006. MY NOTES PRACTICE ANOTHER A uniform beam of length L = 7.45 m and weight 5.25 x 102 N is carried by two workers, Sam and Joe, as shown in the figure below. Determine the force that each person exerts on the beam. Sam Joe +1.00 m +2.00 m L Esam = N Fjoe N 3. [-14 Points] DETAILS SERPSE 10 12.A.P.029. MY NOTES PRACTICE ANOTHER A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam (see figure below). The beam is uniform, weighs 200 N, and is 6.00 m long, and it is supported by a wire at an angle of = 60.0°. The basket weighs 80.0 N. Goodies (a) Draw a free-body diagram for the beam. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) When the bear is at x = 1.00 m, find the tension (in N) in the wire supporting the beam and the components of the force exerted by the wall on the left end of the beam. T = N Fx = N ty = N (c) If the wire can withstand a maximum tension of 775 N, what is the maximum distance (in m) the bear can walk before the wire breaks? m . 4. [-/1 Points] DETAILS SERPSE 10 15.02.014. MY NOTES Which of the following statements is not true regarding a mass-spring system that moves with simple harmonic motion in the absence of friction? The potential energy stored in the system is greatest when the mass passes through the equilibrium position. The total energy of the system is proportional to the square of the amplitude. The total energy of the system remains constant. The energy of the system is continually transformed between kinetic and potential energy. The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position. Need Help? Read It 5. [-/1 Points] DETA 15.00.003. OTE ACTICE ANOTHER A block-spring system vibrating on a frictionless, horizontal surface with an amplitude of 9.5 cm has an energy of 28 J. If the block is replaced by one whose mass is twice the mass of the original block and the amplitude of the motion is again 9.5 cm, what is the energy of the system? O 14 ) O 28 ) O 56 ) O 112) O none of those answers Need Help? Read It 6. [-15 Points] DETAILS SERPSE 10 15.2.OP.003. MY NOTES PRACTICE ANOTHER In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, X = 8.00 cos s (4t + 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 cm S Need Help? Read It Watch It 7. [-17 Points] DETAILS MY NOTES PRACTICE ANOTHER A particle moves along the x axis. It is initially at the position 0.110 m, moving with velocity 0.210 m/s and acceleration -0.310 m/s2. Suppose it moves with constant acceleration for 3.40 s. (a) Find the position of the particle after this time. m (b) Find its velocity at the end of this time interval. m/s We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 3.40 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator. (c) Find the angular frequency of the oscillation. Hint: in SHM, a is proportional to x. /s (d) Find the amplitude of the oscillation. Hint: use conservation of energy. (e) Find its phase constant 4. if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. rad (f) Find its position after it oscillates for 3.40 s. m (9) Find its velocity at the end of this 3.40 s time interval. m/s 8. [-15 Points] DETAILS SERPSE 10 15.2.OP.011.MI. MY NOTES PRACTICE ANOTHER A 0.480-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.6 cm. (Assume the position of the object is at the origin at t = 0.) (a) Calculate the maximum value of its speed. cm/s (b) Calculate the maximum value of its acceleration. cm/s2 (c) Calculate the value of its speed when the object is 8.60 cm from the equilibrium position. cm/s (d) Calculate the value of its acceleration when the object is 8.60 cm from the equilibrium position. cm/s2 (e) Calculate the time interval required for the object to move from x = 0 to x = 2.60 cm. Need Help? Read It Master It ► 9. [-19 Points] DETAILS SERPSE10 15.3.OP.017. MY NOTES PRACTICE ANOTHER A solid metal block with a mass of 3.90 kg is attached to a spring and is able to oscillate horizontally with negligible friction. The block is pulled to a distance of 0.200 m from its equilibrium position, held in place with a force of 21.0 N, and then released from rest. It then oscillates in simple harmonic motion. (The block oscillates along the x-axis, where x = 0 is the equilibrium position.) (a) What is the spring constant (in N/m)? N/m (b) What is the frequency of the oscillations (in Hz)? Hz (c) What is the maximum speed of the block (in m/s)? m/s (d) At what position(s) (in m) on the x-axis does the maximum speed occur? X = + m (e) What is the maximum acceleration of the block? (Enter the magnitude in m/s2.) m/s2 (f) At what position(s) (in m) on the x-axis does the maximum acceleration occur? X = + m (9) What is the total mechanical energy of the oscillating spring-block system (in ])? (h) What is the speed of the block (in m/s) when its position is equal to one-third of the maximum displacement from equilibrium? m/s (i) What is the magnitude of the acceleration of the block (in m/s2) when its position is equal to one-third of the maximum displacement from equilibrium? m/s2 10. [-14 Points] DETAILS SERPSE10 15.A.OP.042. MY NOTES PRACTICE ANOTHER A simple pendulum with a length of 3.23 m and a mass of 6.59 kg is given an initial speed of 2.06 m/s at its equilibrium position. (a) Assuming it undergoes simple harmonic motion, determine its period (in s). (b) Determine its total energy in )). (c) Determine its maximum angular displacement (in degrees). (For large v, and/or small I, the small angle approximation may not be good enough here.) (d) What If? Based on your answer to part (c), by what factor would the total energy of the pendulum have to be reduced for its motion to be described as simple harmonic motion using the small angle approximation where @ < 10°? Need Help? Read It Watch It 11. [-13 Points] DETAILS MY NOTES PRACTICE ANOTHER An oscillator with period 1.6 ms passes through equilibrium at t = 4.8 ms with velocity v = -2.8 m/s. The equation of the oscillator’s motion is x(t) = cm cos(( ]/s)t +

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