A 3.7-kg sphere is suspended by a cord that passes over a 1.7-kg pulley of radius 3.4 cm. The cord is attached to a spring whose force constant is k = 86 N/m as in the figure below. Assume th pulley is a solid disk. www- miw (a) If the sphere is released from rest with the spring unstfetched, what distance does the sphere fall through before stopping? 0.3079 Your response differs from the correct answer by more than 10%. Double check your calculations. m (b) Find the speed of the sphere after it has fallen 25 cm. 1.67 m/s

*16-12. The power of a bus engine is transmitted using the belt-and-pulley arrangement shown. If the engine turns pulley A at w4 = (20t + 40) rad/s, where t is in seconds, determine the angular velocities of the generator pulley B and the air-conditioning pulley C when t = 3 s. 100 mm 25 mm 75 mm вс 50 mm WA

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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.

IP A popular ride at amusement parks is illustrated in the figure ( Eigure 1). In this ride, people sit in a swing that is suspended from a rotating arm. Riders are at a distance of 12 m from the axis of rotation and move with a speed of 35 mi/h. Figure 12 m 1 of 1 T Part A Find the centripetal acceleration of the riders. Express your answer using two significant figures. G| ΑΣΦ 5 Submit Part B Request Answer Find the angle the supporting wires make with the vertical. Express your answer using two significant figures. 195] ΑΣΦΑ Submit Request Answer ?

A ring of radius R is released from rest to roll down a rough incline (assuming there's no energy loss due to friction and there's no slipping in the rolling). Calculate its speed when it reaches the foot of the incline, 4R below the starting point. 4R R (KE+KE,+PE), = = (KE+KE,+PE)f 1 2 0+0+mg4R = ¹1 mv³² + ¹² (mR²³)w² +0 2 2 R

The system is released from rest with the spring initially stretched 2.8 in. Calculate the velocity v of the cylinder after it has dropped 1.5 in. The spring has a stiffness of 4.1 lb/in. Neglect the mass of the small pulley. k = 4.1 lb/in 80 lb

A small solid marble of mass 0.1 kg and radius 0.04 m rolls without slipping along the loop-the-loop track shown in the figure below, having been released from rest somewhere on the straight section of track. From what minimum height above the bottom of the track must the marble be released in order that it just stay on the track at the top of the loop (R = 1.4 m)? |h R O 14.8 m 5.71 m 10.7 m O 8.71 m 3.71 m

You have a pulley 10.2 cm in diameter and with a mass of 2.1 kg. You get to wondering whether the pulley is uniform. That is, is the mass evenly distributed, or is it concentrated toward the center or the rim? To find out, you hang the pulley on a hook, wrap a string around it several times, and suspend your 1.2 kg physics book 1.1 m above the floor. With your stopwatch, you can find that it takes 0.65 s for your book to hit the floor. Use g=9.8 m/s?. What is the moment of inertia if the pulley is uniform? | kg m² What is the actual moment of inertia of the pulley based on your measurement? kg m2 What do you conclude about the pulley? O The pulley is uniform (within 1% of uniform) O The mass of the pulley is concentrated toward the center O The mass of the pulley is concentrated toward the rim