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An object undergoes
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- We do not need the analogy in Equation 16.30 to write expressions for the translational displacement of a pendulum bob along the circular arc s(t), translational speed v(t), and translational acceleration a(t). Show that they are given by s(t) = smax cos (smpt + ) v(t) = vmax sin (smpt + ) a(t) = amax cos(smpt + ) respectively, where smax = max with being the length of the pendulum, vmax = smax smp, and amax = smax smp2.arrow_forwardA pendulum in (Figure 1) has a swinging motion such that 0 = [−0.101 sin(4.95t) + 0.3 cos(4.95t)] rad, where t is in seconds, and the arguments for the sine and cosine are in radians. Assume L = 0.2 m. Figure L 0 1 of 1 Part Determine the magnitude of the velocity of the bob when 0 = 0°. Express your answer to three significant figures and include the appropriate units. v = 0.313 Submit Part B ✓ Correct m a = Determine the magnitude of the acceleration of the bob when 0 = 0°. Express your answer to three significant figures and include the appropriate units. Previous Answers 1.46 Provide Feedback m Submit Previous Answers Request Answer ? X Incorrect; Try Again; 4 attempts remainingarrow_forwardConsider a situation of simple harmonic motion in which the distance between the endpoints is 2.45 m and exactly 9 cycles are completed in 21.5 s. When this motion is viewed as a projection of circular motion, what is the radius, r, and angular velocity, @, of the circular motion? r = m (0) = rad/sarrow_forward
- A vinyl record is played by rotating the record so that an approximately circular groove in the vinyl slides under a stylus. Bumps in the groove run into the stylus, causing it to oscillate. The equipment converts those oscillations to electrical signals and then to sound. Suppose that a record turns at the rate of 33 rev/min, the groove being played is at a radius of 13.5 cm, and the bumps in the groove are uniformly separated by 0.136 mm. At what rate (hits per second) do the bumps hit the stylus?arrow_forwardA particle moves with simple harmonic motion between two points which are 11.8 cm apart. At the instant when the particle is 2.0 cm from one of the points, its acceleration is 48.0 cms−2. Calculate the absolute value of the velocity of the particle at the same instant. Give your answer in m/s.arrow_forwardA pendulum in (Figure 1) has a swinging motion such that 0 = [-0.101 sin(4.55t) +0.3 cos (4.55t)] rad, where t is in seconds, and the arguments for the sine and cosine are in radians. Assume L = 0.4 m. Figure L 0 < 1 of 1 Part A Determine the magnitude of the velocity of the bob when 0 = 0º. Express your answer to three significant figures and include the appropriate units. v= Part B li Submit a = Value Submit μА Request Answer Determine the magnitude of the acceleration of the bob when 0 = 0°. Express your answer to three significant figures and include the appropriate units. Provide Feedback μA Value Units Request Answer ? Units ?arrow_forward
- A particle moves along a curve whose parametric equations are x = 3e¬4, y = 4 sin 3t, z = 5 cos 3t where t is the time. Find the magnitudes of the velocity at t=0. a) 10.42 b) 11.42 c) 12.42 d) 13.42arrow_forwardA particle starts from the origin at t = 0 with a velocity of (16 - 12) m/s and moves in the xy plane with a constant acceleration of = (3.0 - 6.0) m/s2. What is the speed of the particle at t = 2s?arrow_forwardThe position of a particle is given by r →(t) = A (cos ωti ^ + sin ωtj ^), where ω is a constant. (a) Show that the particle moves in a circle of radius A. (b) Calculate d r → /dt and then show that the speed of the particle is a constant Aω. (c) Determine d2 r → /dt2 and show that a is given by ac = rω2. (d) Calculate the centripetal force on the particle. [Hint: For (b) and (c), you will need to use (d/dt)(cos ωt) = −ω sin ωt and (d/dt)(sin ωt) = ω cos ωt.arrow_forward
- A particle moves with simple harmonic motion in a straight line. At time t = 0, the acceleration is 3 m/s2 , the velocity is 1 m/s and the displacement is -0.30 m. Find the period of motion, in seconds.arrow_forwardGiven a particle whose motion represented by the equation s=20t+4t=3t^3.What is the maximum speed reached by the particle?arrow_forwardSuppose a teacher is riding a Ferris wheel. The maximum height they attain is 30 m and theminimum height is 6 m. The time it takes to make one full rotation is about 5 minutes. Determine:a/ The periodb/ The amplitudec/ A possible equation that models this situation, if the time starts at the minimum height.arrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning