When a body of mass 0.25 kg is attached to a vertical massless spring, it is extended 5.0 cm from its unstretched length of 4.0 cm. The body and spring are placed on a horizontal frictionless surface and rotated about the held end of the spring at 2.0 rev/s. How far is the spring stretched?
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- A 4.00 kg mass is attached to a vertical rod by the means of two 1.25 m strings which are 2.00 m apart. The mass rotates about the vertical shaft producing a tension of 80.0 N in the top string. (a) What is the tension on the lower string? (b) How many revolutions per minute does the system make?A thin, light wire is wrappedaround the rim of a wheel (Fig.). Thewheel rotates without friction about a stationaryhorizontal axis that passes through the centerof the wheel. The wheel is a uniform diskwith radius R = 0.280 m. An object of massm = 4.20 kg is suspended from the free end ofthe wire. The system is released from rest andthe suspended object descends with constant acceleration.If the suspended object moves downwarda distance of 3.00 m in 2.00 s, what is themass of the wheel?The figure shows a conical pendulum, in which the bob (the small object at the lower end of the cord) moves in a horizontal circle at constant speed. (The cord sweeps out a cone as the bob rotates.) The bob has a mass of 0.025 kg, the string has length L = 1.2 m and negligible mass, and the bob follows a circular path of circumference 0.69 m. What are (a) the tension in the string and (b) the period of the motion? Сord L. Bob (a) Number i Units (b) Number i Units
- 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 small box with a mass of 6.61 kgkg is being swung around on the end of a string which has a length, L=L=1.52 mm . The box has a tangential velocity of 3.20 m/sm/s and is moving on a level, horizontal surface which has a co-efficient of kinetic friction of 0.345 and a co-efficient of static friction of 0.397.1.0m 3.0m 0.5m mi m, PA N, 5. The drawing above shows two objects on a board supported at two locations. The m; = 40 kg (centered over P), m2=20 kg and m3=10 kg. a. Show the forces acting on the board below with arrows with labels beginning at their approximate point of application (see example for the force exerted by m;). (Don't forget the gravitational forces acting on the board.) P F1
- The cube in the figure is given a push up the incline so that its initial velocity is 9.00 m/s. What distance along the incline (in m) does the cube move before coming to rest? Assume the surface is frictionless, and e = 24.0°.A 200 gram mass hangs from a 0.70m long string. The mass is made to rotate while tracing out a circle in the horizontal plane at 1.0m/s. What angle does the string make with respect to vertical.A 3.72 kg iron box is suspended from a spring with a spring constant of k=18 N/m. The mass is pulled 0.35 m downward from its equilibrium position and allowed to oscillate. a) what will the angular velocity be for this iron box? b) with what period will the iron box oscillate?
- 3. The member OA rotates in vertical plane about a horizontal axis through O with a constant counter clockwise velocity w=3 rad/s. As it passes the position 0=0, a small mass m is placed upon it at a radial distance r=0.5 m. If the mass is observed to slip at 0=37°, find the coefficient of friction between the mass and the member. Answer: uk = 0.1875 Solution ӨZorch, an archenemy of Superman, decides to slow the Earth's rotation to once per 39.5 h by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, because he knows Zorch can only exert a force of 3.20 107 N (comparable to a Saturn V rocket's thrust). Assume the Earth's initial rotation is exactly once per 24.0 h to find how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains. The Earth's mass is 5.98 1024 kg and its radius is 6.38 106 m.)One end of a string is wrapped several times around a pulley of mass 0.92 kgkg that is oriented vertically. The other end of the string is connected to a block of mass 0.35 kg, which is then slowly lowered until the string becomes taut. After which the person lets go of the block completely, thus allowing the block to descend and the pulley to rotate in unison. What is the magnitude of the acceleration of the block after the person has let go?