Slide 1 / 43 AP Physics C Work And Energy With Calculus Slide 2 / 43 An object moves according to the function x = t 5/2 1 where x is the distance traveled and t is the time. Its kinetic energy is proportional to A t 2 t 5/2 B t 3 C t 3/2 D t° (kinetic energy is constant) E Slide 3 / 43 2 Which of the following best describes the relationship between force and potential energy? A Force is the anti-derivative of potential energy Force is the negative gradient of potential energy B Potential energy is the negative gradient of force C Potential energy is the derivative of force D E Force is the anti-derivative of potential energy
Slide 4 / 43 3 A student throws a ball of mass m upward where the initial potential energy is 0. At a height H the ball has a potential energy of U and is moving upward with a kinetic energy of Ke. Ignoring air resistance, the maximum height achieved by the ball is most nearly A (Ke-U)/mg (U-Ke)/mg B (U+Ke)/mg C mg/(U-Ke) D E mg/(U+Ke) Slide 5 / 43 4 A box of mass m is lifted a vertical distance h in time t with a constant velocity. The power supplied by the lifting force is approximately A mght mgh/t B zero C mgt/h D mg/ht E Slide 6 / 43 5 A 5kilogram ball moves in the x direction where x represents the ball’s position. The potential energy U of the ball in joules is given as a function by: U(x) = 4x 2 3x + 2. The force on the particle at x = 4 meters is A 29 N in +x direction 29N in -x direction B 108 N in -x direction C 45 N in x direction D E 108 N in +x direction
Slide 7 / 43 6 A student pushes a box across a rough, flat surface at a constant speed v. The box has a mass m, and the coefficient of sliding friction is represented by µ. The power supplied by the person to the box is A 0 µmg/v B µv/mg C mg/µv D µmgv E Slide 8 / 43 The force exerted by a spring is given by: F=kx 4 /2. If 7 k is 100 N/m find the work done from x=0 to x=2. A 100 J 320 J B 800 J C 1600 J D 2400 J E Slide 9 / 43 8 A man lifts a mass m at constant speed to a height h in time t. How much work is done by the weight lifter? A mgt zero B mgh C mgh/t D cannot be determined E
Slide 10 / 43 It takes a force F given by F = 20x 12x 2 to stretch an 9 irregular spring by a distance x, where F is in newtons and x is in meters. What is the change in potential energy when the spring is stretched 3 meters from its equilibrium position? A 18J 28J B 56J C 64J D 80J E Slide 11 / 43 10 On top of a skyscraper of height H, a ball of mass m is thrown directly downward with an initial speed v o . If the ball reaches the ground with a speed v f , the energy lost to friction is approximately 2 -v f 2 ) mgh- (1/2) m(v o A 2 +v f 2 ) mgh+ (1/2) m(v o B 2 -v o 2 ) C mgh+ (1/2) m(v f 2 +v o 2 ) mgh+(1/2) m(v f D 2 -v o 2 )-mgh (1/2) m(v f E Slide 12 / 43 11 A ball is attached to a string rotates in a complete circle. The work done during each revolution is A 0 U B U+Ke C Ke D E Ke-U
Slide 13 / 43 12 Potential energy of two molecules is given by: U= 2/r 7 -4/r 5 . If r is the distance between two molecules what is the force acting on the particles if r=1m A 0.75 N B 0.67 N 2 N C 6 N D 10 N E Slide 14 / 43 13 A force of 40 N compresses a spring with a spring constant 80 N/m. How much energy is stored in the spring? A 10 J 15 J B 20 J C 25 J D 30 J E Slide 15 / 43 14 When the object of mass m 1 descends to a distance h, the potential energy of the system has decreases by (m 1 – m 2 )gh A m 1 gh B M 1 C (m 1 + m 2 )gh M 2 ½(m 1 + m 2 )gh D 0 E
Slide 16 / 43 15 What is the instantaneous power delivered by gravity to a 6kg block 4 seconds after it has fallen from rest? A 2400 W 1000 W B 800 W C 1200 W D 2000 W E Slide 17 / 43 If F(x)=2x 3 -3x 2 what is the work done from x=1 to x= 16 2? A 0.5 J B 0.8 J 2 J C 12 J D 0 J E Slide 18 / 43 17 A 5 kilogram block is pushed horizontally across a rough surface with a coefficient of kinetic friction of 0.2 by a force F moving at 3 m/s. The work that is done by the force in 20 seconds is A 200 J 400 J B C 600 J 800 J D 1000 J E
Slide 19 / 43 18 The graph represents the force exerted on a particle. What is the work done on the object from x=0 to x= 4 m? A 8 J 10 J B 15 J C 16 J D 20 J E Slide 20 / 43 19 What is the work done on the object from x=0 to x=6 m? A 4 J B 6 J 10 J C 12.5 J D 25 J E Slide 21 / 43 20 A constant force supplies an average power of 8 watts to a box during a certain time interval. If the box has an average speed of 4 meters per second and the force acts in the same direction as motion of the object, the magnitude of the force is A 8 N 6 N B 4 N C 2N D E 1N
Slide 22 / 43 21 Questions 21-23 A ball of mass m is tossed from roof of height h with an initial velocity v o . What is the kinetic energy of the ball at the top of the roof? A 0 mgh B 2 C ½ mv o 2 mgh-½ mv o D 2 mgh+½ mv o E Slide 23 / 43 22 Questions 21-23 A ball of mass m is tossed from roof of height h with an initial velocity v o . What is the potential energy of the ball when it hits the ground? A 0 mgh/2 B 2 ½ mv i C 2 mgh/2+½ mv i D 2 mgh+½ mv i E Slide 24 / 43 23 Questions 21-23 A ball of mass m is tossed from roof of height h with an initial velocity v o . What is the kinetic energy of the ball right before it strikes the ground? A 0 mgh B 2 ½ mv i C 2 mgh-½ mv i D 2 mgh+½ mv i E
Slide 25 / 43 24 The following graphs represent the net force F as a function of displacement x for an ball that moves in a straight line. Which graph best represents the force that will cause the least change in the kinetic energy of the object from x = 0 to x = x 1 ? D B E A C Slide 26 / 43 25 Questions 25-27 A block is attached to a spring that oscillates in simple harmonic motion. At which point is the kinetic energy of the ball at maximum? A Point A B C A Point B B Point C C Points A&B D Kinetic energy is the same at all points E Slide 27 / 43 26 Questions 25-27 A block is attached to a spring that oscillates in simple harmonic motion. What happens to the potential energy as the ball passes from point A to point B? A increases B C decreases A B C stays the same zero D not enough information E
Slide 28 / 43 27 Questions 25-27 A block is attached to a spring that oscillates in simple harmonic motion. Which of the following is true about the system? Potential energy is never A equal to Kinetic energy Potential energy is equal to B Kinetic energy at all points The system will eventually C stop moving There is a restoring force D Both B&D E B C A Slide 29 / 43 28 A 4 kg mass is moving with a velocity given by v (t) = ¼t 4 . At t= 1 s, the instantaneous power delivered by the net force is A 1 W 3 W B 12 W C 14 W D 20 W E Slide 30 / 43 29 What is the instantaneous power delivered by the net force at the t = 2 s to a 2 kg mass moving according to x(t) = t 3 /3? A 2 W 10 W B 16 W C 24 W D 32 W E
Slide 31 / 43 30 A particle of mass m follows the potential energy graph as shown below. The mass is initially at rest at R O . Determine the particle’s speed at position 4ro. U(R) A 4U B U C 4R R R D E Slide 32 / 43 31 A particle of mass m follows the potential energy graph as shown below. The mass is initially at rest at R O . The function U(r) = ar-3/2 + b represents the potential energy of a particle, where b and c are constants, which of the following is an expression for the force on the particle? U(R) A 4U B U C 4R R R D E Slide 33 / 43 32 The force exerted by a non-uniform spring is F = -kx 3 . The maximum displacement of the spring is x = 2 m. The spring constant of the spring is 36 N/m and the mass of the block is .5 kg. Find the total energy of the system. A 12 J 144 J B 36 J C 120 J D 432 J E
Slide 34 / 43 33 The force exerted by a non-uniform spring is F = -kx 3 . The maximum displacement of the spring is x = 2 m. The spring constant of the spring is 36 N/m and the mass of the block is .5 kg. Find the maximum speed of the system. A 9.8 m/s 24 m/s B 15 m/s C D 20 m/s 27 m/s E Slide 35 / 43 34 A block of mass m slides down an incline and experience a friction force with a coefficient of kinetic friction µ on the ramp and the track it follows. The block comes to rest at point 4. At which point is the kinetic energy the greatest? 1 A Point 1 Point 2 B H Point 3 3 C 4 2 Points 4 D Between Point 1&2 E Slide 36 / 43 35 A block of mass m slides down an incline and experience a friction force with a coefficient of kinetic friction µ on the ramp and the track it follows. The block comes to rest at point 4. Which of the following best represents the energy lost to friction from point 1 to point 4? 1 A µmgH MgH B H √ (2gH) C 3 4 2 2mg/H D 2gH E
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