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(b) Plug the expressions from (a) into the conservation of energy equation KE+ PEKE+ PE (Cancel mass everywhere) (c) Solve for h algebraically. h- (d) Plug in numbers to calculate h m 7. A 1.70 kg block slides on a horizontal, frictionless surface until it encounters a spring with a force constant of 955 N/m. The block comes to rest after compressing the spring a distance of 4.60 cm. Use the steps below to find the initial speed of the block. (a) Match the expressions for the initial and final potential and kinetic energies. PE 0 KE 0 PE 1/2πιν;" 1/2kx KE (b) Plug the expressions from (a) into the conservation of energy equation. KEPE, KE+PE (c) Solve for vi algebraically. v.=. (d) Plug in numbers for v V₁ = m/s (Make sure that x is in meters). 8. A snowboarder with initial speed of 5 m/s goes up a rise 1 m high. What is her speed at the top of the rise? (a) Match the expressions for the initial and final potential and kinetic energies. PE 1/2mv 0 PE₁ 1/2mx, mgh KE (b) Plug the expressions from (a) into the conservation of energy equation KE PEKE + PE (Cancel mass) (c) Solve for the final speed. vr. algebraically. (d) Plug in the numbers for v Vy= m/s ΚΕ 9. A ball is the ¿poods (8)
9. A ball is thrown straight up into the air and reaches a height of 50 m. What was the initial speed? (a) Match the expressions for the initial and final potential and kinetic energies. PE 0 ΚΕ 0 PE 1/2mv KE mgh (b) Plug the expressions from (a) into the conservation of energy equation KE+ PEKE+PE (Cancel mass) (c) Solve for the initial speed, vi, algebraically. Vi m/s (d) Plug in the numbers for vi. (e) Sketch a graph of kinetic energy, potential energy and total mechanical energy as functions of time.. Energy 10. A horizontal spring stretches 0.2 meters when a force of 10 N is applied. When the spring is in its relaxed-equilibrium state, it is struck by a 1.5 kg mass traveling at 0.80 m/s. How far is the spring depressed? (a) Calculate the spring constant from the information in the first sentence. AF k= N/m Ar (b) Match the expressions for the initial and final potential and kinetic energies. PE, 0 0 KE PE₁ 1/2mv/? ½kx² KE (c) Plug the expressions from (b) into the conservation of energy equation KE+PEKE+ PE (Cannot Cancel mass) X= (d) Solve for the spring compression, x, algebraically. (e) Plug in the numbers for to get x. x m/s