For this problem, examine the figure above with a disk sitting on a table. The mass of the disc is 0.29 kg. There is a light string connected to the side of the disk passing through a hole in the centre of the table. Friction between the string and the hole at the center is negligible. Initially, the disk starts off at a radius of 35 cm from the center moving in a circular path at a speed of 0.1 m/s. The string is then pulled down-ward 6 cm. How much work is done on the disc by the Force?
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- An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.9 rad, b = 0.75 rad/s2 and c = 0.025 rad/s3.Randomized Variables a = 1.9 radb = 0.75 rad/s2c = 0.025 rad/s3 1) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1? 2) Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values. 3) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?In the figure, a small 0.176 kg block slides down a frictionless surface through height h = 0.427 m and then sticks to a uniform vertical rod of mass M = 0.352 kg and length d = 2.46 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ.A spring with spring constant k and equilibrium length zero is attached tothe top of a frictionless hoop of radius R. The spring is stretched and connected to a bead of mass m at the bottom of the hoop. At t = 0 the bead is given an initial speed v0 and the bead moves up the hoop. Find the speed of the bead as a function of position on hoop v(θ).
- A mass m=10kg is fastened to a light spring k=380N/m by a light that passes over a pulley. Assume the pulley is a uniform cylinder of mass Mp=5kg and radius R=0.2m and rotates without friction. The mass is released from rest when the spring is unstretched. The spring remains firmly fixed to the floor and to the string. What is the angular velocity of the pulley when the mass has fallen a distance h=0.4m stretching the spring.A 24 g block sits at the center of a turntable that rotates at 80 rpm. A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable. Calculate the turntable's angular speed when the block reaches the outer edge. Treat the turntable as a solid disk with mass with mass 200 g and diameter 54.0 cm. Express your answer in revolutions per minute.The 18-cm-diameter disk in (Figure 1) can rotate on an axle through its center. For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Nutcracker. Figure 30 N 457 5 cm 5 cm 20 N -30 N X 20 N 1 of 1 >
- A thin rod of length 0.632 m and mass 66.5 g is suspended freely from one end. It is pulled to one side and then allowed to swing like a pendulum, passing through its lowest position with angular speed 1.35 rad/s. Neglecting friction and air resistance, find (a) the rod's kinetic energy at its lowest position and (b) how far above that position the center of mass rises.One end of a cord is fixed and a small 0.400-kg object is attached to the other end, where it swings in a section of a vertical circle of radius 1.50 m, as shown in the figure below. When θ = 23.0°, the speed of the object is 5.50 m/s. An object is swinging to the right and upward from the end of a cord attached to a horizontal surface. The cord makes an angle θ with the vertical. An arrow labeled vector v points in the direction of motion. (a) At this instant, find the magnitude of the tension in the string.Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N(b) At this instant, find the tangential and radial components of acceleration. at = Your response differs from the correct answer by more than 100%. m/s2 downward tangent to the circle ac = Your response differs from the correct answer by more…A uniform thread of linear mass density λ=2. 0 g/m passes through a fixed ideal pulley. At its ends, the thread is stacked into two heaps that do not interfere motion of the thread. A beetle of mass m=80 g tries to manage itself at a constant height on the thread by adjusting its speed relative to the thread
- Chapter 11, Problem 066 GO Your answer is partially correct. Try again. In the figure, a small 0.109 kg block slides down a frictionless surface through height h = 1.46 m and then sticks to a uniform vertical rod of mass M = 0.218 kg and length d = 1.55 m. The rod pivots about point O through angle e before momentarily stopping. Find 0. Number Units (degrees) em the tolerance is +/-2% em Click if you would like to Show Work for this question: Open Show WorkA cylinder has a cone removed from it. The cylinder and the conical hole have the same radius (2.06 meters) and height (4.56 meters). The cylinder has a density of 447 kg/m3. What is the rotational inertia of the cylinder with the cone removed in kg m2? You can set your origin at the tip of the cone, which is also the center of the base of the cylinder.A tetherball is connected to the top of a pole with a rope that is 2.58m long and swings around the pole at an angle of θ = 33.4 degrees between the pole and the rope. Calculate the speed of the tetherball in meters/second, but only enter in the numerical value, do NOT enter units.