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Transcript
SPH 4U Hooke’s Law Problems 1. The force applied to a dynamics cart is measured with a stretched spring. What is the acceleration of a 2.0 kg cart on a flat, frictionless surface if pulled by a spring, of force constant 40 N/m, stretched by a constant amount of 8.0 cm? (1.6 m/s2) 2. What is the force constant of a Hooke's Law spring if the extension of the spring is 0.15 m when 0.72 J of potential energy is stored in it? (64 N/m) 3. A 5.0 g pellet is placed in the barrel of a toy gun and is propelled by a spring of force constant 50 N/m that has been compressed 20 cm and then released. Calculate the maximum velocity of the pellet when shot horizontally. (20 m/s) 4. The force-deformation graph for a non-Hooke's Law spring is shown. (a) How much work must be done to compress the spring 0.16 m? (b) How much potential energy is stored in the spring at this compression? (c) What speed would a 1.0 kg mass acquire if it were placed next to this compressed spring, on a smooth, horizontal surface, and then released? (0.72 J, 0.721 J, 1.2 m/s) 5. The spring in a toy gun has a force constant of 500 N/m. It is compressed 5.0 cm, and a ball of mass 10 g is placed next to it in the barrel. (a) What is the ball's maximum velocity, when the trigger releases the spring? Assume that there is no friction, and that the gun barrel is level. (11 m/s) (b) Determine the muzzle velocity if an average retarding force of 0.80 N acts on the ball, and the barrel is 0.25 m long. (9.2 m/s) 6. A 3.0 kg ball is dropped from a height of 0.80 m onto a vertical spring of force constant 1200 N/m. What is the maximum compression of the spring? (0.22 m) 7. A linear elastic spring is 15.0 cm long. When the upper end is held in the hand and a 500 g mass is suspended from the lower end, its length becomes 22.0 cm. If the hand is now jerked quickly upward, the spring first extends to a length of 28.5 cm; then the mass starts to move up. The hand is then held still. (a) Calculate the acceleration with which the mass first begins to move. (9.1 m/s2) (b) Calculate the speed of the mass when the length of the spring is 22.0 cm again. (0.77 m/s) (c) Calculate the length of the spring when the mass comes to rest at its highest point. (15.5 cm) \sph4U\moment\565331089