Slide 4 / 36 3 A 5kilogram ball moves in the x direction where x - - PDF document

AP Physics C

Work and Energy Calculus Based

Multiple Choice www.njctl.org

Slide 1 / 36

1 An object moves according to the function x = t7/2 where x is the distance traveled and t is the time. Its kinetic energy is propor­ tional to: A B C D E

Slide 2 / 36

2 Which of the following best describes the relationship between force and potential energy? A Force is the anti­derivative of potential energy B Force is the negative gradient of potential energy C Potential energy is the negative gradient of force D Potential energy is the derivative of force E Force is the derivative of potential energy

Slide 3 / 36

3 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: U(x) = 4x2 ­ 3x + 2. The force on the particle at x = 4 m is: A 29 N in ­x direction B 29N in +x direction C 108 N in ­x direction D 45 N in x direction E 108 N in +x direction

Slide 4 / 36

4 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 B µmg/v C µv/mg D mg/µv E µmgv

Slide 5 / 36

5 The force exerted by a spring is given by: F = kx4/2. If k is 100 N/m, find the work done by the spring on a mass from x = 0 m to x = 2 m. A 100 J B 320 J C 800 J D 1600 J E 2400 J

Slide 6 / 36

6 A worker lifts an object of mass m at constant speed to a height h in time t. How much work is done by the worker on the object? A mgt B zero C mgh D mgh/t E mgt/h

Slide 7 / 36

7 A spring force is given by the formula F = 20x ­ 12x2 , where F is in N and x is in m. What is the change in potential energy when the spring is stretched 3 m from its equilibrium position? A 18 J B ­18 J C 56 J D ­56 J E 64 J

Slide 8 / 36

8 On top of a skyscraper of height H, a ball of mass m is thrown directly downward with an initial speed vo. What is the speed of the ball before it strikes the ground? Ignore air resistance. A B C D E

Slide 9 / 36

9 A ball attached to a string rotates in a complete circle at a constant

• speed. The work done during each revolution is (U ­ potential

energy, KE ­ kinetic energy): A 0 B U C U + KE D KE E KE ­ U

Slide 10 / 36

10 The potential energy of two molecules is given by: If r is the distance between two molecules what is the force acting

• n the particles if r=1 m?

A 0.75 N B 0.67 N C 2 N D ­6 N E 10 N

Slide 11 / 36

11 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 B 15 J C 20 J D 25 J E 30 J

Slide 12 / 36

12 What is the power delivered by gravity to a 6 kg block 4 s after it has fallen from rest? A 2400 W B 1000 W C 800 W D 1200 W E 2000 W

Slide 13 / 36

13 If F(x) = 8x3­3x2 what is the work done from x =1 m to x =2 m? A 0.5 J B 0.8 J C 2 J D 12 J E 23 J

Slide 14 / 36

14 A 2 kg block is pushed horizontally across a rough surface with a coefficient of kinetic friction of 0.2, at a constant speed of 4 m/s, by a force F. The work that is done by the force in 5 s is: A 20 J B 40 J C 60 J D 80 J E 100 J

Slide 15 / 36

15 A constant force supplies an average power of 8 W to a box during a certain time interval. If the box has an average speed of 4 m/s, and the force acts in the same direction as motion of the object, the magnitude of the force is: A 1 N B 2 N C 4 N D 6 N E 8 N

Slide 16 / 36

16 Which of the following is true about an oscillating system in SHM? A Potential energy is never equal to kinetic energy B Potential energy is equal to kinetic energy at all points C Potential energy decreases all the time D Kinetic energy increases all the time E Maximum potential energy is equal to maximum kinetic energy

Slide 17 / 36

17 A 4 kg mass is moving with a velocity given by v (t) = 1/4t4. At t= 1 s, the instantaneous power delivered by the net force is: A 1 W B 3 W C 12 W D 14 W E 20 W

Slide 18 / 36

18 What is the instantaneous power delivered by the net force at t = 2 s to a 2 kg mass moving according to x(t) = 1/3t3? A 2 W B 10 W C 16 W D 24 W E 32 W

Slide 19 / 36 Slide 20 / 36

20 The function U(r) = αr­3/2 + β represents the potential energy of a particle, where α and β are positive constants, which of the following is an expression for the force on the particle? A B C D E

Slide 21 / 36

21 A mass moves under the influence of a potential energy given by: U(x) = x3 ­ 2x2 At x = 2 m, the force on the mass will be: A 4 N, + direction B 4 N, ­ direction C 3 N, + direction D 3 N, ­ direction E 7 N, + direction

Slide 22 / 36

22 A 6 kg object’s potential energy is represented by: U(r) = 9r2+4. Find the acceleration of the object at r = 2 m A ­4 m/s2 B 4 m/s2 C ­6 m/s2 D 6 m/s2 E 12 m/s2

Slide 23 / 36

23 A restoring force F = ­2x3 acts on an object, where x is the displacement of the object from its equilibrium position. How much work must be done by an external force to move the object from x= 0 to x= 2 m? A 2 J B 24 J C 8 J D 10 J E 15 J

Slide 24 / 36

24 How much work is done by an external force in stretching a spring from x = 0 to x = 0.2 m, whose restoring force varies according to the following formula: F(x) = ­(6 N/m)x + (30 N/m2)x2? A ­0.04 J B 0.04 J C ­0.16 J D 0.16 J E 0.08 J

Slide 25 / 36 Slide 26 / 36

26 The potential energy of a spring is given by the following formula: U(x) = 1/3αx3 ­ βx, where α and β are positive constants. Which of the following represents the restoring force of the spring? A 3αx2 – β B ­3αx2 + β C 2αx3 ­ βx D 3αx ­ β E ­αx2 + β

Slide 27 / 36

Slide 28 / 36

28 The gravitational force between a spaceship and Earth is given by the formula: F =­GMm/r2 . Which of the following represents the potential energy of the spaceship/Earth system, assuming that U = 0 when r ⇒ ∞. A B C D E

Slide 29 / 36

29 A conservative force parallel to the x­axis moves a particle along the x­axis. The potential energy of the particle is given by U(x) = 1/4αx4, where α = 0.5 J/m4. What is the force on the particle when it is located at x = 2 m? A ­4 N B 4 N C 8 N D ­8 N E 10 N

Slide 30 / 36

Slide 31 / 36

31 A conservative force parallel to the x­axis moves a particle along the x­axis. The potential energy as a function of position is presented by the graph. The particle is released from rest at point

• A. What is the approximate force on the particle when it passes

point B? A 3 N B 1 N C ­3 N D 6 N E ­6 N

Slide 32 / 36

32 A conservative force parallel to the x­axis moves a particle along the x­axis. The potential energy as a function of position is presented by the graph. The particle is released from rest at point

• A. At what location(s) is the particle is in stable equilibrium?

A x = 1.0 m only B x = 2.0 m only C x = 4.0 m only D x = 2.0 m and x = 4 m only E x = 2.0 m and x = 5.6 m only

Slide 33 / 36

33 A conservative force parallel to the x­axis moves a particle along the x­axis. The potential energy as a function of position is presented by the graph. The particle is released from rest at point

• A. What is the largest value of x reached by the particle during this

motion? A 5.6 m B 4.0 m C 6.9 m D 8.0 m E 2.0 m

Slide 34 / 36

34 A conservative force parallel to the x­axis moves a particle along the x­axis. The potential energy as a function of position is presented by the graph. The particle is released from rest at point

• A. At what location(s) is the particle is in unstable equilibrium?

A x = 1.0 m only B x = 2.0 m only C x = 4.0 m only D x = 2.0 m and x = 4 m only E x = 2.0 m and x = 5.6 m only

Slide 35 / 36

35 A conservative force parallel to the x­axis moves a particle along the x­axis. The potential energy as a function of position is presented by the graph. The particle is released from rest at point

• A. What is the approximate force on the particle when it passes

point D? A 2 N B ­2 N C ­3 N D ­4 N E ­6 N

Slide 36 / 36