(Solved): The diagram shows a ball initially placed on a compressed spring. When the ball is released, it is ...

The diagram shows a ball initially placed on a compressed spring. When the ball is released, it is projected vertically upward. Diagram is not to scale. Refer to the above diagram to answer this question. A \( 2.50 \mathrm{~kg} \) ball is placed on a spring system composed of two springs. The outer spring has an elastic constant of \( 4.5 \mathrm{~S} \times 10^{3} \mathrm{~N} / \mathrm{m} \) while the inner (longer) spring has an elastic constant of \( 6.80 \times 10^{3} \mathrm{~N} / \mathrm{m} \). The ball begins at a height \( \left(h_{1}\right) \) of \( 5.00 \mathrm{~cm} \) above the table. When the ball is \( 15.0 \mathrm{~cm}\left(h_{2}\right) \) above the table, the outer spring is fully extended. The ball continues to be pushed upward by the inner spring until, at a distance of \( 22.0 \mathrm{~cm}\left(h_{3}\right) \) above the table, the inner spring is fully extended. At the instant that the inner spring has reached its full length, the speed of the ball as it leaves the springs is \( \mathrm{m} / \mathrm{s} \). (Record your three-digit answer on the answer sheet.) The diagram shows the free body diagram of the forces acting on mass which at the instant shown is moving up a frictionless inclined plane. Which of the following statements apply to the description of the state of the energy of for the mass? 1. The gravitational potential energy of the mass is increasing. II. The gravitational potential energy of the mass is decreasing. III. The kinetic energy of the mass is increasing. VV.The kinetic energy of the mass is decreasing. a. I and III b. II and III c. I and IV d. II and IV Two frictionless dynamics carts (A and B) are coasting on a horizontal surface. Cart A, with a mass of \( 3.60 \mathrm{~kg} \), is travelling at \( 6.00 \) \( \mathrm{m} / \mathrm{s} \) [E]. Cart B has a mass of \( 2.40 \mathrm{~kg} \) and is travelling at \( 3.00 \mathrm{~ms} /[\mathrm{E} \) ]. When cart \( A \) catches up to, collides with, and sticks to cart B, the two carts are moving at the same speed. If the collision resulted in a loss of \( 6.93 \mathrm{~J} \) of mechanical energy, what is the final speed of the two carts? a. \( 4.80 \mathrm{~m} / \mathrm{s} \) b. \( 4.20 \mathrm{~m} / \mathrm{s} \) c. \( 5.20 \mathrm{~m} / \mathrm{s} \). d. \( 3.90 \mathrm{~m} / \mathrm{s} \) A \( 1.5 \mathrm{~m} \) long pendulum with a \( 3.2 \mathrm{~kg} \) bob, is pulled sideways from its rest position and then released. When it passes through its rest position, the tension in the string that supports the bob is \( 50 \mathrm{~N} \). The height above its rest position from which the pendulum bob was released must be m. Assume that frictional forces are negligible. (Record your two-digit answer on the answer sheet.) The radius of the motion of a child's swing is \( 2.75 \mathrm{~m} \). A \( 25.0 \mathrm{~kg} \) child on this swing is pulled sideways until the angle that the swing ropes make with the vertical is \( 32.0^{\circ} \). Assuming that the forces of friction are negligible, then, the force, in scientific notation, that the seat of the swing must exert on the child as she passes through the lowest point of the arc is \( b \quad 10^{\text {w }} \mathrm{N} \). The value of \( \boldsymbol{b} \) is (Record your three-digit answer on the answer sheet.) The diagram shows a pendulum bob that has been pulled to the right by an angle \( \theta \). Diagram is not to scale. A \( 2.85 \mathrm{~m} \) long pendulum has a \( 5.60 \mathrm{~kg} \) bob. The bob is pulled to the right and given a push back toward its rest position so that when the bob passes through its rest position, its kinetic energy is \( 85.0 \mathrm{~J} \). If when the pendulum bob passes through a dosition that is at a distance of \( d m \) to the right of its rest position, it has a kinetic energy of \( 35.0 \mathrm{~J} \). The value of \( d \) is (Record your three-digit answer on the answer sheet.)