Your Name:  _______________________                             PHY203

                                                                                                            Exam #3

Student ID:  ________________________                            Chapters 6-8

                                                                                                            Thurs., 11/01/01

 

 

 

Lecture Time:         9 a.m             1p.m.             2p.m.       3p.m.       Honors         

 

 

 

 

 

 

 

Score:

 

 

1          _________________

 

 

 

2          _________________

 

 

 

3          _________________

 

 

 

+ 1

 

 

Total              _______________

 

 

1.         A ball of mass 5.0 kg is traveling in the negative y direction. At a height of 2.0m above the ground the speed of the ball is 5.0m/s.  At a height of 1.0m above the ground the ball hits an uncompressed massless spring.  The spring is compressed by 0.5m before the ball stops (momentarily), as shown below.

 

 

a.         Calculate the kinetic, K, potential, U, and total energy, E, of the system for the ball at a height of 2.0m. (Take U=0 at ground level, y=0.)

 

 

 

 

 

 

 

 

 

 

 

b.        Using conservation of energy, calculate the speed of the ball when it just hits the spring at a height of 1.0m.

 

 

 

 

 

 

 

 

c.         Using conservation of energy when the ball stops, calculate the spring

constant of the spring.

2.         A block of mass 5.0 kg is traveling in positive x direction on a frictionless surface with a speed of 8.0m/s. At point A, the block encounters a rough patch of 2.0m in length with a kinetic coefficient of friction of 0.2. At point B then it begins sliding up a frictionless ramp until it stops (before sliding back down) at point C.

 

 

a.         Calculate the kinetic, K, potential, U, and total energy, E, of the system for the block at point A. (Take y=0 at ground level.)

 

 

 

 

 

 

 

b.        Calculate the mechanical energy lost to friction between points A and B.

 

 

 

 

 

 

 

 

c.         Calculate the velocity of the block at point B.

 

 

 

 

 

 

 

d.         Using conservation of energy, find the height, H, at which the block stops (at point C).

3.         A 3.0kg block is traveling in the positive x-direction on a horizontal, frictionless surface at an initial speed of 5.0m/s. The block explodes and breaks into 2 pieces. One piece (m1 = 2.0kg) shoots off in the negative y direction with speed of 4.0m/s.  (Note: all of the action below is on a horizontal plane-i.e.the blocks do not fall; gravity is not important.)

 

a.         Using the coordinate system shown above, calculate the initial momentum and kinetic energy of the block before the explosion.  Write the momentum in vector notation.

 

 

 

 

 

 

 

 

 

b.        Find the velocity of the second block ( m2) after the explosion and write it in vector notation.

 

 

 

 

 

 

 

 

 

 

 

c.           Calculate the final kinetic energy of the system.


5.         A block of mass m=7.0 kg is traveling in the positive x direction on a frictionless surface with a speed of vo=4.0m/s. The block encounters a force F=50N which is applied over a distance of d=2m at an angle of 60o with respect to the horizontal, as shown below.  After the force has been removed, the block hits a spring which has a force constant of k=500 N/m.

 

 

a.         Calculate the kinetic energy, K, of the block at point A.

 

 

 

 

 

 

b.        Calculate the work, W, done on the block by the force, F.

 

 

 

 

 

 

 

 

c.         Using work and energy, calculate the velocity, v, of the block at point B.

 

 

 

 

 

 

 

 

d.         Calculate the distance, x, by which the spring is compressed by the block before the block stops (momentarily).

 

 

 

6.         A 2.0kg bob is at rest at the end of a string of length L=0.5m.  An explosion occurs which causes the bob to break into 2 pieces. One piece (m1=0.5kg) shoots off in the positive x direction with a speed of 6.0m/s.  The other piece (m2=1.5kg) remains attached to the string as shown below.

 

 

a.        Calculate the linear momentum, p2, of the second piece of the bob (m2) just after the explosion and write it in vector notation.

 

 

 

 

 

 

 

 

 

b.        Calculate the speed, v2, and kinetic energy, K2, of the m2 piece just after the explosion.

 

 

 

 

 

 

 

 

 

c.           Calculate the height, H, of the second piece when it stops (momentarily) and find the angle, q, the string makes with the vertical at that point. 


5.         A block of mass 7.0 kg is traveling in the positive x direction on a frictionless surface with a speed of 8.0m/s. At point A, the block encounters a rough patch of 3.0m in length with a kinetic coefficient of friction of 0.25. At point B it slides up a circular, frictionless ramp with a radius of 1.0m.

 

 

a.         Calculate the kinetic, potential and total energy of the system for the block at point A (take y=0 at ground level and ignore the height of the block).

 

 

 

 

 

b.        Calculate the energy lost to friction between points A and B.

 

 

 

 

 

 

 

 

c.         Calculate the velocity of the block at point B.

 

 

 

 

 

 

d.         Using conservation of energy, find the velocity when the block is at a height of 1.0m (at point C as shown above).

 

 

 

 

 

e.         Find the normal force that the ramp exerts on the block at this point.

PHY203

Exam #3, F/01

Crib Sheet

Chapters 6-8

 

(Note: Use 9.81 m/s2 for g, the acceleration due to gravity.)

 

 

 

(Note: Bold letters indicate vectors below.)

 

 

F = ma

 

spring force: F = -kDx , where k is the spring constant

 

weight: W = mg

 

friction force: 

      kinetic        fk = mkFn , where Fn is the normal force and mk is                                                        the kinetic frictional coefficient

      static          fs < msFn,       fsmax = msFn

 

 

uniform circular motion

centripetal force:  F = mv2/r

 

centripetal acceleration:  a = v2/r

 

 

momentum

 p = mv

 

Conservation of momentum: pinitial = pfinal

 

Work and Energy

 

W = F . x  = Fxcosq

 

Work done by friction = fkDs

 

Kinetic Energy: K = 1/2mv2

 

Potential Energy:       Uspring = 1/2kx2

                                    Ugrav     = mgh 


Your Name:  _______________________                              PHY203

                                                                                                            Final Exam

Student ID:  ________________________                            Chapters 1-14

                                                                                                            Thurs., 12/13/01

 

 

 

Lecture Time:         9 a.m             1p.m.             2p.m.       3p.m.       Honors         

 

 

 

 

1          _________________                                7          __________________

 

 

2          _________________                                8          __________________

 

 

Part 1      ____________                                            Part 4       __________

 

 

 

 

3          _________________                                9          __________________

 

 

4          _________________                                10       __________________

 

 

Part 2      ____________                                            Part 5     ____________

 

 

 

5          _________________

 

 

6          _________________                                Total    _______________

 

 

Part 3      ____________

9.         A block of unknown material weighs 5N in air and 4.55N when completely submerged in water.

 

 

 

a.         Calculate the buoyant force.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b.        Calculate the density of the unknown material (use rwater = 1x103 kg/m3).

10.      A block oscillates with an amplitude of A=5.8 cm attached to a horizontal spring of force constant k=1.8 kN/m.  Its maximum speed is vmax=2.20 m/s.

 

 

a.         Calculate the angular frequency, w, of the motion of the block.

 

 

 

 

 

 

 

 

 

 

 

 

b.        Calculate the period, T, of the motion of the block.

 

 

 

 

 

 

 

c.         Calculate the mass, m, of the block.

PHY203

Final

Crib Sheet, P. 1

 

speedAV = (total distance traveled)/Dt

vAV = Dx/Dt

aAV = Dv/Dt

vInst = dx/dt

aInst = dv/dt

 

For constant acceleration:

xf = xo + vot + (1/2)at2

 

vf = vo + at

 

vf2 = vo2 + 2a(xf - xo)

 

For a vector A with magnitude A and direction q (measured counterclockwise with respect to the x-axis):

 

Ax = Acos(q)

Ay = Asin(q)

A = (Ax2 + Ay2)1/2

tan(q) = Ay/Ax

 

For a vectors A,B,C with magnitudes A,B,C:

If C = A x B; C = ABsinq    with direction of C given by the right hand rule

 

(Note: Use 9.81 m/s2 for g, the acceleration due to gravity.)

 

spring force: F = -kDx , where k is the spring constant

 

momentum

 p = mv

Conservation of momentum: pinitial = pfinal

 

torque:                                    t = r x F

angular momentum:              L = r x p         = Iw

parallel axis theorem:            I = ICM + Mh2

I solid sphere = 2/5MR2

 

Oscillations:

If x = Acos(wt + d); then v = -w Acos(wt + d)

for a spring, w =(k/m)1/2