Standing on the side of a bridge, a person uses a sling shot pulled back 20 centimeters to shoot a rock with a mass of 250 grams almost straight up into the air which then falls into the water below. The pebble traveled a maximum height of 4.0 meters above the level of the person's hand, which is 8.5 meters above the water. Find the spring constant of the elastic band of the sling shot and the speed at which the pebble hits the water. Ignore air resistance. Solve using conservation of energy principles and the various forms of kinetic and potential energies.

A 2.0 kg ball is launched by means of a vertically oriented spring with spring constant k = 16.0 N/cm. The spring is compressed 10.0 cm before the launch. (a) What is the maximum speed of the ball during this launch? (b) What is the maximum height the ball reaches? (Consider y = 0 to be the equilibrium height of the spring)

A 1.50-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of v. = 2.80 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). a m Vj = V=0 k (a) Find the distance of compression d (in m). m (b) Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d). m/s (c) Find the distance D (in m) where the object comes to rest. m (d) What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest…

A block with a mass of 30.0 kilograms (kg) is held against a spring with a force constant of k = 1.25×105 N/m. The spring is initially compressed 17.5 centimeters (cm) from equilibrium. Then the block is released, setting it into motion. The block initially slides along a frictionless surface, but then it encounters a 1.50 meter long rough patch where the coefficient of kinetic friction is 0.134. It then slides down a frictionless ramp, which is tilted at an angle of 19.5 degrees and has a length of 2.50 meters. How fast is the block moving when it reaches the bottom of the ramp? Give your answer in meters per second (m/s). Hint: use WNC = ΔK + ΔU.