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Problems 1-3

A train travels along a straight level track, in three phases, as follows:

Phase 1 - The train starts at rest at point A and accelerates uniformly, traveling 500 meters to point B. The train passes point B with a velocity of 15 meters /second.
Phase 2 - After passing point B, the train maintains a constant velocity, and reaches point C in 40 seconds.
Phase 3 - After passing point C, the train decelerates at a uniform rate of 0.10 meters/second ², and passes point D with a velocity of 10 meters/second.
1. The acceleration of the train I phase 1, in SI units, is closest to:
A) 0.10        B) 0.22          C)0.34             D)0.48             E) 0.60
v²-v_o²=2a(x-x_o)                 a = 15²/2.500 = 0.225
2. The distance traveled at constant velocity, in SI units, is closest to:
A) 600         B) 800 C) 1000 D) 1100 E)1200
x-x_o = v.t                  x-x_o = 15.40 = 600
3. The time of travel between point C and point D, in SI( units, is closest to:
A) 50          B) 55              C) 60                  D) 65            E)70
v = v_o -a.t              t =- (v - v_o)/a = -(10-15)/0.1 = 50

Problems 4 - 6

The ball, in flight as shown in the figure, takes 4.96 s to strike the ground.

4. The initial height of the ball, y in m is closest to:
A) 20                 B) 24.4                  C) 32.2                   D)36.6                 E) 40.0
y - y_o = v_o sin50.t - gt²/2                    0 - y_o = 25.3sin50.4.96 - 9.8.4.96²/2 = - 24.4
5. The maximum height relative to ground reached by the ball Y_max in meters is closest to:
A) 33.6               B) 38.8                C) 43.6                 D) 50.2                   E) 56.4
v_y = v_o.sinf -g.t at maximum v_y = 0 so t = 25.3sin50 / 9.8 = 1.978 s
y = y_o+ v_o sin50.t - gt²/2 = 24.4 + 25.3.sin50.1.978 - 9.8.1.978²/2 = 43.56
6. The horizontal distance, x, traveled by the ball in meters is closest to:
A) 60.4               B) 68.7               C) 74.6              D) 80.7                    E) 88.4
x-x_o = v_xcos50.t = 25.3.cos50.4.94 = 80.7 s

Problems 7 - 9

The 25 -N force remains horizontal and constant at all times.
The coefficient of static friction m _s = 0.4
The coefficient of kinetic friction m _k = 0.2
7. The weight of the load W for the 16 N block to be on the verge of slipping upward in SI units is closest to:
A) 20         B) 22            C) 24            D) 26              E) 30
For W: T = W for 16 N block: - 16 - F_smax + T = 0 so - 16 - 25.0.4 + W = 0 and W = 16 + 10 = 26
8. The weight of load W is 10 N. The magnitude and direction of the friction force in SI units is closest to:
A) 6, down             B) 6, up              C) 8,down                D) 8, up               E) 10, up
Is it static friction force up? - 16 + 10 + F_s = 0 F_s = 6 and F_smax = 25.0.4 = 10 good
Is it static friction force down? - 16 + 10 - F_s = 0 F_s = - 6 negative sign shows wrong answer.  Assumed good guess.
9. The load W is removed completely. The magnitude and direction of the acceleration of the 16 N block in SI units is closest to:
A) 3.0, up           B) 3.0, down              C) 3.7, up               D) 3.7, down            E) 6.7, down
Assuming acceleration down    - 16 + 25.0.2 = - m.a            a = -11/-1.6 = 6.875

Problems 10 -12

10. The tension in cord 1 in SI units is closest to:
A) 45           B) 50            C) 55             D) 60           E) 65
T₁ - 4.9.8 = 4.4                  T₁ = 55.2
11.  The tension in cord 2 in SI units is closest to:
A) 27.4         B) 279             C) 284            D) 289           E) 294
T₂ - T₁ - 40.9.8.0.2 = 40.4                     T₂ = 160 + 40.9.8.0.2 + 55 = 293.4
12. The mass of block A in kg is closest to:
A) 46.4              B) 50.6             C) 54.8               D) 58.2               E) 62.5
T₂ - M_A.9.8 = - M_A.4                       M_A = 294/5.8 = 50.6

Problems 13 - 15

A vertical shaft has a horizontal cross - arm from which a 0.75 kg ball is suspended by two wires as shown. The shaft is set into uniform rotation such that the centripetal acceleration of the ball is 5.5 m/s².

13. The linear speed of the ball, in SI units, is closest to:
A) 1.3           B) 1.5            C) 1.7            D) 1.9              E) 2.1
v² / R = 5.5 v = (5.5.0.8)^0.5 = 2.1
14. The rate of rotation, in revolutions per minute, is closest to:
A) 25             B) 28             C) 32            D) 36                E) 41
w = v/R = (2.1/0.8)(60/2p) RPM = 25
15. The tension in wire 1, in SI units, is closest to:
A) 5.2            B) 5.8             C) 6.3               D) 6.9               E) 7.5
T₁sin37 = m.a_{r =} 0.75.5.5 T₁ = 0.75.5.5 / 0.6 = 6.875
Problems 16 - 18

A block of mass 6 kg is pushed 10 m, up a sloping surface of a plane inclined at an angle of 37⁰ to the horizontal by a constant force of 60 N acting parallel to the plane. The force of friction on the block is 20 N and the block starts from rest at point A.

16. The work done by the 60 N force in Joules is:
A) 353             B) 200              C) 480            D) 600              E) 720
60.10 = 600
17. The work done by the friction force in Joules is:
A) +200              B) -200             C) +353               D) -600            E) +600
-200
18. The speed of the block when it reaches point B in SI units is closest to:
A) zero             B) 1.48               C) 3.97              D) 4.62                E) 5.50
FBD then 60 - 20 - 6.9.8.sin37 = 6.a              a = 0.77             v²-v_o²=2a(x-x_o)                   v  = (2.0.77.10)^0.5 = 3.95

Problems 19 - 21

A 5 -kg block is moving along a horizontal plane with a velocity of 3 m/s when it strikes a spring of force constant 900 N/m. The spring is compressed 20 cm before the velocity of the block is reduced to zero.

19. The kinetic energy of the block the instant before impact in SI units is:
A) 10.5            B) 14.5             C) 17.5            D) 22.5              E) 25.5
¹/₂.5.3² = 22.5
20. The elastic potential energy of the spring in SI units when the velocity of the block is zero is:
A) 10            B) 14              C) 18               D) 2               E) 26
¹/₂.k.x² = 18
21. The work done on the block by the friction force in SI units is:
A) 4.5            B) 6.5              C) 8.5             D) 10.5                E) 12.5
22.5 - 18 = 4.5

Problems 22 - 23
A 2-lb ball is dropped from a height of 16 ft. and rebounds to a height of 9 ft. The ball is in contact with the floor for 0.02 sec. Note: g = 32 ft/s².

22. The magnitude of the change in momentum of the ball in SI units is:
A) 0.5                B) 1.5              C) 2.5                D) 3.5            E) 4.5
v = (2.g.y)^0.5 then Dp = m.(2.g.H)^0.5 + m. (2.g.h)^0.5 = 112 / 32 = 3.5 slug.ft/s when convert to SI:     0.5     
23. The magnitude of the average force exerted on the ball in SI units is:
A) 25             B) 75             C) 125               D) 175               E) 225
F = Dp/Dt         F = 25

Problems 24 - 25
The two blocks A nad B are on a collision course, as shown in the figure. After the collision, block B acquires a velocity of 4 m/s directed toward the right. It is found that 51.75 J (Joules ) of energy is "lost " in the collision. Find:

24. The magnitude and direction of the velocity of block A after the collision in SI units:
A) 1 m/s, +x               B) 1 m/s, -x            C) 2 m/s, +x               D) 2 m/s, -x                E) 3 m/s, -x
20M - 5.2M = M.v + 2M.4                     v = +2
25. The value of M in kg is:
A) 0.125          B) 0.25                C) 0.30              D) 0.35              E) 0.40
¹/₂.M.20² + ¹/₂.2M.5² - 51.75 = ¹/₂.M.2² + ¹/₂.2M.4²                M = 0.25

Problems 26 - 27
The wheel shown is rotating in a counter - clockwise direction with constant angular acceleration. A point on the rim of the wheel has a radial acceleration of 40 cm/s² magnitude when at position A. When the point moves to position B, the radial acceleration is 90 m/s².

26. The angular acceleration of the wheel is SI units (rad/s²) is closest to:
A) 0.250               B) 0.314               C) 0.628                 D) 1.20             E) 1.59
v_A²/R = 0.4 v_B²/R = 0.9        >>           v_A = (0.4.0.1)^0.5 = 0.2             v_B = (0.9.0.1)^0.5 = 0.3            w = v/R        w_A= 2          w_B = 3
w_B² - w_A² = 2.a.Df           a = (w_B² - w_A²) / 2.Df                Df = p/2                a = 1.59
27. The time for the point to move from A to B is closest to:
A) 0.250             B) 0.314              C) 0.628              D) 1.20                E) 1.59
w_B - w_A = a.t      >>         t = 0.62

Problems 28 - 30

The diagram shows a pulley wheel, which can rotate about a frictionless axis through its center and perpendicular to the plane of the paper. The inner radius, R₁ = 0.3 m: the outer radius, R₂ = 0.6 m. The 4-kg mass accelerates downward at the rate of 3.0 m/s². A cord is wound around the inner pulley hub and force of 42.4 N is applied as shown.

28. The tension in the outer cord in SI units is closest to:
A) 20.4          B) 27.2              C) 39.2              D) 42.4              E) 50.0
T - 4.9.8 = 4.(-a)    >>       T = 39.2 - 12 = 27.2
29. The net torque on the pulley wheel in Nm ( assume counterclockwise moments to be positive ) is closest to:
A) -1.2          B) +1.2           C) -3.6            D) +3.6            E) +4.2
T.0.6 - T₂.0.3 = 27.2.0.6 - 42.4.0.3 = 3.6
30. The angular acceleration of the pulley wheel in SI units is closest to:
A) 1           B) 2            C) 3           D) 4              E) 5
a = a/R        >>       a = 3/0.6 = 5
Problems 31 - 33
A man stands on a turntable holding a pair of equal weights , each at a distance of 0.8 m from the axis of rotation of the turntable. The mass of each weight is 4 kg and they can be considered point masses. The moment of inertia of the man and turntable is 3.6 kgm² and is to be taken as constant
The man is given an angular velocity of 4.5 rad/s with the weights extended. He next pulls the weights in until they are 0.12 m from the axis. Friction is to be neglected.

31. The initial moment of inertia of the system (man and weights with the weights extended in sI units is closest to
A) 3.6           B) 5.2             C) 6.2             D) 7.4            E) 8.7
I = 3.6 + 2.4. (0.8)² = 8.72
32. The initial angular momentum of the system in SI units is closest to:
A) 16.2         B) 23.4          C) 27.9           D) 33.3               E) 39.2
L = I.w = 8.72.4.5 = 39.24
33. The angular velocity of the system once the man pulls the weights in towards the axis of rotation in SI units is closest to:
A) 4.5             B) 6.8              C) 8.6             D) 10.6                 E) 12.4
I = 3.6 + 2.4. (0.12)² = 3.715
I_o.w _o = 39.24 = I.w = 3.715.w       >>      w = 10.56

_{Problems 34 - 36}

_{A 4m uniform strut is pivoted at P. The strut is kept horizontal by means of a 3m cable attached to the strut at Q and anchored in the ceiling at S. The weight of the strut is 200 N. A 500 N weight is suspended from Q.
Let Px and Py be the components of the pivot force, and let T be the tension in the cable.
34.  The tension in the cable in SI units is closest to:
A) 575        B)600        C) 650}         D) 693         E)714
200.2 + 500.4 -Tcos30.4 = 0                           T = 692
35. The horizontal force the pivot at P exerts on the strut in SI units is closest to:
A) 340              B) 346                C)358                 D)366                     E)374
Tcos60 = 692.0.5 = 346
36. The vertical force the pivot at P exerts on the strut in SI units is closest to:
A) 100               B)150                    C)300               D)450                      E)700
200.2 - P_y.4 = 0        >>            P_y = 100
37. If the mass of a satellite is doubled while the radius of its orbit remains constant, the speed of the satellite is:
A) increased by a factor of 8        B) increased by a factor of 2          C) not changed           D) reduced by a factor of 8
E)  reduced by a factor of 2
GmM/R² = mv²/R         v doesn't depend on m - orbiting mass so no change
38. If the mass of a planet is doubled while its radius and the radius of orbit of its moon remain constant, the speed of the moon is:
A) increased by a factor of 1.4            B) increased b a factor of 2           C) not changed          D) reduced by a factor of 1.4
E) reduced by a factor of 2
v = (GM/R)^0.5 v ' = (G2M/R)^0.5 = 2^0.5 v
39. If the mass of the earth is 6.10²⁴ kg, the mass of the moon 7.10²² kg, the radius of the moon's orbit 4.10⁸ m, and the value of the gravitational constant G = 6.10^-11 N.m²/ kg², the force between the earth and the moon is approximately:
A) 5.10⁴ N           B) 2.10²⁰ N               C) 3.10⁵⁰ N                   D) 7.10³⁰ N                 E) 3.10²⁸ N
F = GmM/R² F = 16.10¹⁹

40. Five homogeneous planets have relative masses and sizes as shown in the figure. A body of mass m would weigh least on which planet.

A) 1               B) 2                  C) 3                    D) 4                 E) 5
 
 
 

Quick Answers
Version A

1B, 2A, 3A, 4B, 5C, 6D, 7D, 8B, 9E, 10C, 11E, 12B, 13E, 14A, 15D, 16D, 17B, 18C, 19D, 20C, 21A, 22A, 23A, 24C, 25B, 26E, 27C, 28B, 29D, 30E, 31E, 32E, 33D, 34D, 35B, 36A, 37C, 38A, 39B, 40E.
difference in units
1B, 2A, 3A, 4B, 5C, 6D, 7D, 8B, 9E, 10C, 11E, 12B, 13E, 14A, 15D, 16D, 17B, 18C, 19D, 20C, 21A, 22D, 23D, 24C, 25B, 26E, 27C, 28B, 29D, 30E, 31E,
32E, 33D, 34D, 35B, 36A, 37C, 38A, 39B, 40E