The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in the figure below. If the spring is compressed a distance of 0.200 m and the gun fired vertically as shown, the gun can launch a 22.0-g projectile from rest to a maximum height of 22.0 m above the starting point of the projectile. (a) Neglecting all resistive forces, describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height.

The force on a particle of mass 2.0 kg varies with position according to F(x) = -3.0x² (x in meters, F(x) in newtons). The particle's speed at x = 3.0 m is 6.7 m/s. (a) Calculate the mechanical energy of the particle (in J) using the origin as the reference point. (b) Calculate the mechanical energy of the particle (in J) using x = 5.0 m as the reference point. J (c) Find the particle's speed (in m/s) at x = 2.0 m, using the origin as the reference point. m/s Find the particle's speed (in m/s) at x = 2.0 m, using x = 5.0 m as the reference point. m/s

Ms. Dewitte's son, Theo, slides down a slide, from rest, with a length of 2.00 m at an incline of 50° above the horizontal. He has a mass of 22.0 kg and he reaches the bottom of the slide with a velocity of 2.90 m/s. Briefly explain if total mechanical energy was conserved and what energy transfers otcurred?

A 0.5 kg ball experiences the one-dimensional, conservative force Fx as shown in Figure 1. The corresponding potential energy versus x is is shown in Figure 2. No friction involves throughout the path. The ball has a total energy of 60.0 J and the zero potential reference is at x = 0 m. [Answer in 3 significant figures] F, versus x 30 25 20 15 10 0. -5 0 2. 4 5 -6- 8 - 6. 10 -10 -15 -20 -25 -30 -35 -40 -45 -50 -55 -60 x (m) Figure 1 Conservative force versus position Potential energy versus X 1. 1. 1. 3. (N) *)