A simple pendulum (a mass swinging at the end of a string) wings back and forth in a circular arc. What is the direction of the acceleration of the mass when it is at the ends of the swing? At the midpoint? In each case, explain how you obtain your answer.
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- A light rod is 88 cm long. Its top end is pivoted on a low-friction horizontal axle. The rod hangs straight down at rest with a small massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swing around in full circle. What minimum speed (m/s) at the bottom is required to make the ball go over the top of the circle? Round your answer to 2 decimal places.A 0.500 kg particle moves in a circle of radius 0.150 m at constant speed. The time for 20 complete revolutions is 31.7 s. What is the period T of the motion? What is the speed of the particle?A conical pendulum consists of a ball (mass=3 kg) fixed on the end of a massless cord. The ball moves at a constant velocity of of v=3 m/s in uniform circular motion. The length of the cord is L=5 m. Find the angle a that the cord makes with respect to the the y-axis. g=9.8 m/s^2, r=radius of motion Eq 1: g tan(a)=v^2/r Eq 2: r=L sin(a) Substituting Eq 2 into Eq 1 gives g tan(a)=v^2/L sin(a), which becomes tan(a)sin(a)=v^2/gL or, sin^2(a)/cos(a)=v^2/gL How do I solve for angle a?
- E. The centripetal acceleration of a particle moving in a circle is given by the formula a = s²/r where r is the radius and s is the speed of the particle. a) Consider a as a function of s and r. Compute the differential of a. b) Suppose that the particle is moving with speed 50cm/sec and the radius is 10cm. Use the differential to estimate the change in centripetal acceleration if the radius is changed to 9.80cm and the speed is changed to 51cm/sec. (Answ: 15) c) Suppose that the speed can be measured to within +3% and the radius can be measured to within +2%. Use the differential to approximate the maximum percent error in a. (Hint: The percent error in a quantity is the error in the quantity (da) divided by the quantity (a).) (Ans: 8%)An object is moving counterclockwise around a circular track at a constant speed of 3 m/s. The track is centered at the origin and has a radius of 1 m. What is the object's acceleration vector when it is at point P shown? y. P -(3플)i ○금3 + (3프) i a = +(9) i m Oa = 0 -(9플)iWhile sitting in physics class one day, you begin to ponder the workings of the analog clock on the classroom wall. You notice as the hands sweep in a continuous motion that there are exactly t = 49 minutes left in class. a)Through what angle (in radians) will the second hand turn before the end of class? b)Through what angle (in radians) will the minute hand sweep before the end of class? c)Through what angle (in radians) will the hour hand sweep before the end of class?
- You re out in space, on a rotating wheel-shaped space station of radius 679 m. You feel planted firmly on the floor , due to artificial gravity. The gravity you experience is Earth-normal, that is, g = 9.81 m/s^2. How fast is the space station rotating in order to produce this much artificial gravity? Express your answer in revolutions per minute (rpm). 0.120 rpm 81.6 rpm 0.459 rpm 1.148 rpmAn astronaut lost in space is far from any other mass (i.e.,gravity is negligible). He swings a weight of mass m = 0.5 kg that is tiedto a string, and it undergoes counterclockwise circular motion with aradius r = 2 m. The mass does a revolution once every 3 seconds.a) Draw the velocity and acceleration vectors of mass m at points p1,p2, and p3.b) What is the velocity?c) What is the centripetal force?d) What is the magnitude of the tension force in the string?A model of a helicopter rotor has four blades, each of length 3.4 mm from the central shaft to the blade tip. The model is rotated in a wind tunnel at a rotational speed of 500 rev/minrev/min. 1. What is the linear speed of the blade tip? Express your answer in meters per second. 2. What is the radial acceleration of the blade tip expressed as a multiple of the acceleration due to gravity, gg? Express your answer as a multiple of gg. 3.
- A toy aeroplane of mass m = 1,80 kg is attached to a string of length e = 33.0 m and flys in uniform circular motion in a horizontal plane around the centre of its motion. The plane has an engine which generates thrust that keeps the plane moving at a speed of v = 30.7 km/hr. (a) What is the period of the circular motion? Period = S (b) What is the tension in the string holding the aeroplane in its circular motion? Tension = Part 3) A block sits on a sloping plane that can have its angle to the vertical p varied. The angle o initially starts at a value of 90°, and the slope is raised until at an angle o E 33.2° the block starts to slide down the slope. Calculate the coefficient of static friction for this block on this slope.In the game of tetherball, a ball is hung from a vertical pole via a 0.75m rope. The rope is allowed to pivot freely from the top of the pole so the ball can swing around the pole. If the angle of the rope is 30° with respect to the pole, how much time does it take the ball to make one complete revolution around the pole?Hi, today I had my engineering mechanics 1 test which I completely screwed up. I was quite confident in the uniform circular motion, but I had this problem in my exam which completely confused me. When I read "upward vertical acceleration" my head just start to spin as I couldn't understand what force could cause an upward acceleration. Could you help me with this problem? I bet it is easier than it looks, but still, I am confused about what is asking me and most importantly about the input it is giving me. I don't have my exam paper with me, but on my body diagram, I knew that on the aeroplane were exerted the Force of Contact Fn1 and the Force m1g in the y opposite direction. On the pilot was acting the Force of Contact with the seat of the aeroplane Fn2 and the m2g in the y opposite direction. Here is the problem: During an air show an aircraft comes out of a dive at the bottom of a circular arc at a horizontal speed of 97m/s. In the cockpit the aircraft pilot of mass 58kg…