Consider a mass of 50kg attached to a spring to spring of 1800N/m and placed on a rough surface. The mass is subjected to a force F = 120cos(3t). Find the magnitude of the coefficient of friction if the maximum amplitude is not to exceed 75mm. Hint: μ ≤ 0.104 www F(t) m K -μ
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- A clock pendulum oscillates at a frequency of 2.5 Hz . At t=0, it is released from rest starting at an angle of 16 ∘ to the vertical. Part AIgnoring friction, what will be the position (angle in radians) of the pendulum at t = 0.35 s ?Express your answer using two significant figures. Part bIgnoring friction, what will be the position (angle in radians) of the pendulum at t = 540 s ?Express your answer using two significant figures.A mass M hangs from a spring with a spring constant k. Calculate the frequency and period of oscillation if: m(kg) k(N/m) 5.00E+00 1.00E+01Here is a pendulum, when theta is equal to zero, what angle does the tension in the 10m long cord become zero, if the 5kg mass at the end of the string has a speed of 10 m/s at its lowest point?
- Review.A light spring has unstressed length 15.5 cm.It is described by Hooke's law with spring constant 4.30 N/m. One end of the horizontal spring is held on a fixed vertical axle,and the other end is attched to a puck of mass m that can mow without friction over a horizontal surfaces.The pck is set into motion in a circle with a period pf 1.03 s. (a) Find the extension of the spring x as it depends on m.Evaluate x for (b) m =0.0700kg. (c) m = 0.140 kg (d) m = 0.180 kg (e) m = 0.190 kg (f) describe the pattern of variation of x axis as it depnds on mYou pull on a string with a horizontal force of magnitude F = 40 N that is attached to a block of mass m, = 7.5 kg, then to the axle of a solid cylinder of mass m. = 4.8 kg and radius r = 0.4 m, then to a spring of spring constant k = 140 N/m. This is all done on an inclined plane where there is friction ( 4s = 0.68 and , = 0.31 ), and the incline angle is e = 25 degrees. Everything starts at rest, and the spring is unstretched. The block slides down the plane, the cylinder rolls down the plane (without slipping), and the Cylinder, Spring, and Block on Ramp spring stretches. 000000000- b yb First, what is the speed of the block and cylinder after you have pulled the block and cylinder 86 cm down the plane?A mass of 7 kg hangs from a spring attached to the ceiling. The spring has a spring constant of 500 N/m and it stretches 13.6 cm from its mean position. A student grabs the spring, applies a force and stretches it a further 3.0 cm downwards. The block is released and initially accelerates upward before undergoing simple harmonic motion. Calculate the initial vertical acceleration of the mass. (Units: m/s2 , to 2 sig figs)
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