Slide 1 / 38 Slide 2 / 38 1 A student throws a ball upward where the initial potential energy is 0. At a height of 15 meters the ball has a potential energy of 60 joules and is moving upward with a kinetic energy of 40 joules. AP Physics C Ignoring air resistance, the maximum height achieved by the ball is most nearly Work And Energy Without Calculus A 10 m 20 m B C 25 m 30 m D 40 m E Slide 3 / 38 Slide 4 / 38 2 A box of mass m is lifted a vertical distance h in 3 A crate is lifted by a force F which is greater in time t with a constant velocity. The power magnitude than the crate’s weight W. The change supplied by the lifting force is approximately in kinetic energy of the crate during this time is equal to the A mght A work done by the net force (F W) mgh/t B B work done by F zero C C work done by W mgt/h D the change in momentum of the rock before and after this mg/ht E D time the change in the potential energy of the rock before and E after this time. Slide 5 / 38 Slide 6 / 38 4 A constant force supplies an average power of 8 5 A pencil is moved from point A to point B along a watts to a box during a certain time interval. If the curved path. The work done by the gravitational box has an average speed of 4 meters per second force on the pencil depends on which of the and the force acts in the same direction as motion following: of the object, the magnitude of the force is A the velocity of the object as it moves between A and B the positions of points A A 8 N B and B 6 N B the path taken between A C and B 4 N C both the positions of A and B and the path taken between D them 2N D 1N E the nature of the external force that moves the object from E A to B
Slide 7 / 38 Slide 8 / 38 6 A man lifts a mass m at constant speed to a 7 A 3 m long frictionless pendulum of swings with an height h in time t. How much work is done by the amplitude of 10°. At its equilibrium position the kinetic man? energy of the pendulum is 20 J. What is the potential energy of the pendulum when the kinetic energy is 5 J? A mgt zero B 3.3 J A mgh C 5 J B mgh/t D C 6.7 J cannot be determined E D 10 J 15 J E Slide 9 / 38 Slide 10 / 38 9 A spring has a spring constant of 100 N/m and is 0.1 8 On top of a 300meterhigh skyscraper, a 2kilogram ball is thrown directly downward with an initial m long when unstretched. One end is attached to a center post that is free to rotate on a frictionless table speed of 20 meters per second. If the ball reaches top. The other end is attached to 2 kg disc moving in the ground with a speed of 60 meters per second, uniform circular motion, which stretches the spring by the energy lost to friction is approximately 0.05 m. What is the centripetal force on the disc? A 0J 1800 J B A 0.5 N 2300 J C B 5 N D 2800 J C 10 N 3300 J E 500 N D E 1,000 N Slide 11 / 38 Slide 12 / 38 10 A spring has a spring constant of 100 N/m and is 0.1 11 A student pushes a box across a rough, flat m long when unstretched. One end is attached to a surface at a constant speed of 1 meter per second. center post that is free to rotate on a frictionless The box has a mass of 50 kilograms and the table top. The other end is attached to 2 kg disc coefficient of sliding friction is 0.2. The power moving in uniform circular motion, which stretches supplied by the student to the box is the spring by 0.05 m. A 0 What is the work done on the disc by the spring during one full circle? 5 W B 50 W C A 0 J D 100 W 0.5 J B 200 W E 186 J C 314 J D 628 J E
Slide 13 / 38 Slide 14 / 38 12 A ball of mass m is suspended at the end of a 13 An ideal massless spring is fixed to a wall at one massless string of length L as shown below. This end and attached to a block of mass M on the pendulum is lifted to a 45 o with the verticle and other end. The spring oscillates with amplitude A released. At the low point of its swing, the speed of on a frictionless, horizontal surface. The the ball is maxixmum speed of the block is vm. The spring constant of the spring is A √( gL) A Mg/A √( 2gL) B L Mg/2A B √( (2 - √ 2)gL) C 2 /2A C Mv m gL D 2 /A 2 Mv m D E (1/2)gL 2 /2A 2 Mv m E Slide 15 / 38 Slide 16 / 38 15 A cart of mass M travels along roller coaster that is shown 14 When the object of mass m1 descends to a above. It consists of a frictionless ramp of height 4R distance h, the potential energy of the system connected to a frictionless loop of diameter 2R and a decreases by frictionless hill of height R. After the hill it comes to a frictionless horizontal track collides with a spring with a force constant K that is attached to the wall. After the A (m 1 – m 2 )gh collision with the spring the cart compresses the spring m 1 gh B and stops at point E. M 1 (m 1 + m 2 )gh C At which point is the potential energy of the cart the greatest? D ½(m 1 + m 2 )gh M 2 A Point A 0 E B Point B C Point C D Point D E Point E Slide 17 / 38 Slide 18 / 38 16 A cart of mass M travels along roller coaster that is shown 17 A cart of mass M travels along roller coaster that is shown above. It consists of a frictionless ramp of height 4R above. It consists of a frictionless ramp of height 4R connected to a frictionless loop of diameter 2R and a connected to a frictionless loop of diameter 2R and a frictionless hill of height R. After the hill it comes to a frictionless hill of height R. After the hill it comes to a frictionless horizontal track collides with a spring with a frictionless horizontal track collides with a spring with a force constant K that is attached to the wall. After the force constant K that is attached to the wall. After the collision with the spring the cart compresses the spring collision with the spring the cart compresses the spring and stops at point E. and stops at point E. At which point is the kinetic energy of the cart the greatest? How fast is the cart traveling at Point D? A Point A √( 2gR) A B Point B 2 √( 2gR) B C Point C √( 3gR/2) C D Point D √( 6gR) D E Point E 2 √( gR) E
Slide 19 / 38 Slide 20 / 38 18 A cart of mass M travels along roller coaster that is shown 19 A cart of mass M travels along roller coaster that is shown above. It consists of a frictionless ramp of height 4R above. It consists of a frictionless ramp of height 4R connected to a frictionless loop of diameter 2R and a connected to a frictionless loop of diameter 2R and a frictionless hill of height R. After the hill it comes to a frictionless hill of height R. After the hill it comes to a frictionless horizontal track collides with a spring with a frictionless horizontal track collides with a spring with a force constant K that is attached to the wall. After the collision with the spring the cart compresses the spring force constant K that is attached to the wall. After the and stops at point E. collision with the spring the cart compresses the spring and stops at point E. At Point C what is the direction of the cart's acceleration? Determine the cart's acceleration at Point C. D B C E None A A 0.25 g B 2 g C 3 g D 4 g E None Slide 21 / 38 Slide 22 / 38 20 A cart of mass M travels along roller coaster that is shown 21 A cart of mass M travels along the roller coasters that is shown below. It consists of a frictionless ramp of height 4R above. It consists of a frictionless ramp of height 4R connected to a frictionless loop of diameter 2R and a connected to a frictionless loop of diameter 2R and a frictionless hill of height R. After the hill it comes to a frictionless hill of height R. After the hill it comes to a rough horizontal track. frictionless horizontal track collides with a spring with a force constant K that is attached to the wall. After the collision with the spring the cart compresses the spring What is the coefficient of kinetic friction so that the cart stops at the end of the rough track? and stops at point E. A 0.25 What is the maximum compression in the spring? B 0.5 √( 2mgR/k) A C 1 √( mgR/k) B D 2 2 √( mgR/k) C E 4 2 √( 2mgR/k) D E 8mgR/k Slide 23 / 38 Slide 24 / 38 22 A 5 kilogram block is pushed horizontally across a 23 A ball swings from a simple pendulum in simple rough surface with a coefficient of kinetic friction harmonic motion as shown below. of 0.2 by a force F moving at 3 m/s. The work that is done by the force in 20 seconds is At which point is the kinetic energy of the ball at its maximum? A 200 J A Point 1 400 J B Point 2 B C 600 J 1 5 C Point 3 800 J D 5 m 4 Point 4 2 D 1000 J E Point 5 E 3
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