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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_forward8:47 4 Consider the following motion: (a) You start at the origin then walk 2 steps in the positive x direction. (b) You then walk 3 steps in the negative x direction. (c) You then walk 4 steps in the negative x direction. (d) You then walk 5 steps in the positive x direction. Document (11) 1. Write the displacement for each part of the motion Axa = Axb= Axc= Axd= 2. Show the addition of the 4 displacement vectors in a diagram below. Draw the vectors tip to tail. Then connect the tail of the first vector to the tip of the last vector to get the resultant vector. 3. What is the magnitude of the resultant vector (i.e., what do you get when you add all 4 displacements together)? 4. How far away from the origin do you end up? Part B: Vectors in Two Dimensions 1. You walk from the origin 11 steps East, then turn and walk 9 steps North. a. How far from the origin do you end up? a b. Draw a vector that starts from the origin, has a length of 11 units and points due East. Label this vector A.…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_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_forwardQ. 3) A ball of mass 500 g is fastened to a string 1.2 m long and suspended from a fixed- point P to make a conical pendulum as shown in the figure. The ball describes a circle of radius r. Find: (a) The radius of the horizontal circle (b) The tension in the string. (c)The velocity of the ball. (d) The period of motion of the ball P 150 ?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