(Solved): The diagram shows the free body diagram of the forces acting on mass which at the instant shown is ...

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. IV.The kinetic energy of the mass is decreasing. a. I and III b. II and IIII 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. \( 3.90 \mathrm{~m} / \mathrm{s} \) The diagram shows a block that is sliding down a frictionless hill. Diagram is not to scale. Refer to the above diagram to answer this question. The above diagram shows a \( 6.20 \mathrm{~kg} \) block sliding down a frictionless hill. At the instant the block passes over a point at the tip of \( \vec{h}_{1} \), it has a speed of \( 1.71 \mathrm{~m} / \mathrm{s} \) and is \( 3.96 \mathrm{~m} \) above the base of the hill. What is the mechanical energy of the block at that instant? a. \( 240 \mathrm{~J} \) b. \( 250 \mathrm{~J} \) C. \( 260 \mathrm{~J} \) d. \( 270 \mathrm{~J} \) The diagram shows a skateboarder starting to roll down a hill. Assume that the skateboard rolls with negligible friction. Diagram is not to scale. Refer to the above diagram to answer this question. When a \( 72.0 \mathrm{~kg} \) skateboarder passes point \( \mathrm{P} \), he has \( 125 \mathrm{~J} \) of kinetic energy. If \( h_{1} \) is \( 4.25 \mathrm{~m} \) and \( h_{2} \) is \( 3.45 \mathrm{~m} \), what is the speed of the skateboarder as he passes point Q? a. \( 4.38 \mathrm{~m} / \mathrm{s} \) b. \( \quad 6.92 \mathrm{~m} / \mathrm{s} \) c. \( 8.00 \mathrm{~m} / \mathrm{s} \) d. \( 9.13 \mathrm{~m} / \mathrm{s} \) 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 diagram shows a mass that is used to compress a spring on a plane. When the mass is released, the spring propels the mass up the plane. Diagram is not to scale. Refer to the above diagram to answer this question. A \( 4.50 \mathrm{~kg} \) mass is shown at rest against a spring which has an elastic constant of \( 7.60^{\circ} 10^{3} \mathrm{~N} / \mathrm{m} \). At that instant, the spring is compressed a distance \( (x) \) of \( 15.0 \mathrm{~cm} \) from its rest position and is \( 0.350 \mathrm{~m} \) above the base of the frictionless inclined plane. When the mass is released, the spring accelerates it up the plane. What will be the speed of the mass when it reaches a height of \( 1.20 \mathrm{~m} \) above the base of the plane? a. \( 15.1 \mathrm{~m} / \mathrm{s} \) b. \( 4.02 \mathrm{~m} / \mathrm{s} \) C. \( 4.62 \mathrm{~m} / \mathrm{s} \) d. \( \quad 6.12 \mathrm{~m} / \mathrm{s} \)