"The girl has a mass of 55 kg and center of mass G. If she is swinging to a maximum height defined by 0=40°, use conservation of energy to determine her speed when she passes through the lowest point, where = 0. B 2 m 30° 30°
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- A space probe is fired as a projectile from the Earths surface with an initial speed of 2.00 104 m/s. What will its speed be when it is very far from the Earth? Ignore atmospheric friction and the rotation of the Earth. P11.26 Ki+Ui=Kf+Uf12mvi2+GMEm(1rf1ri)=12mvf212vi2+GME(01RE)=12vf2orvf2=v122GMEREandvf=(v122GMERE)1/2,vf=[(2.00104)21.25108]1/2m/s=1.66104m/sThe "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper end. Each arm supports a seat suspended from a cable 5.00 m long, the upper end of the cable being fastened to the arm at a point 3.00 m from the central shaft. (Figure 1) Find the time of one revolution of the swing if the cable supporting a seat makes an angle of 30.0∘ with the vertical.To form a pendulum, a 0.024 kg ball is attached to one end of a rod of length 0.70 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i Units (b) Number i Units (c) Number i Units
- To form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.84 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i (b) Number (c) Number (d) Units Units Units #To form a pendulum, a 0.092 kg ball is attached to one end of a rod of length 0.62 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same?To form a pendulum, a 0.050 kg ball is attached to one end of a rod of length 1.2 m and negligible mass, and the other end of the rod is mounted on a pivot. The rod is rotated until it is straight up, and then it is released from rest so that it swings down around the pivot. When the ball reaches its lowest point, what are (a) its speed and (b) the tension in the rod? Next, the rod is rotated until it is horizontal, and then it is again released from rest. (c) At what angle from the vertical does the tension in the rod equal the weight of the ball? (d) If the mass of the ball is increased, does the answer to (c) increase, decrease, or remain the same? (a) Number i 4.8e0 (b) Number i 1.4e0 (c) Number i 19. (d) increase Units Units Units m/s N °(degrees)
- Suppose that a simple pendulum consists of a small 73 g bob at the end of a cord of negligible mass. If the angle 0 between the cord and the vertical is given by e = (0.099 rad) cos[(5.1 rad/s)t+¢], what are (a) the pendulum's length and (b) its maximum kinetic energy? (a) Number Units (b) Number UnitsSuppose thata simple pendulum consists of a small 73 g bob at the end of a cord of negligible mass. If the angle 0 between the cord and the vertical is given by e = (0.099 rad) cos[(5.1 rad/s) t + p], what are (a) the pendulum's length and (b) its maximum kinetic energy? (a) Number Units (b) Number UnitsA simple pendulum is released from rest when the mass is 33.1 cm above its lowest point. What is the speed of the suspended mass at the bottom of its swing? g= 9.80 m/s2 and ignore air restistance. No mass was given.
- Suppose that a simple pendulum consists of a small 79 g bob at the end of a cord of negligible mass. If the angle 0 between the cord and the vertical is given by 0 = (0.041 rad) cos[(5.9 rad/s) t+ p], what are (a) the pendulum's length and (b) its maximum kinetic energy? (a) Number i Units (b) Number i UnitsA block of mass m= 6.0 kg is attached to a spring (K=4.0 N/cm) by a rope that hangs over á pulley of mass M= 8.0 Kg.If the system starts from rest with the spring unextended, find the speed of the block af ter it falis 1.0 m. Take the pulley as a disk,so 1= MR?/2. kjane, whose mass is 50.0−kg needs to swing across a river (having width D)filled with person-eating crocodiles to save Tarzan from danger. She must swing into a wind exerting constant horizontal force F on a vine having length L and initially making an angle θ with the vertical Take D=50.0 m,F=110 N, L=40.0 m and θ=50.0 o With what minimum speed must Jane begin her swing to just make it to the other side?