380 AP PHYSICS 1 AND 2 AP PHYSICS 1—TEST 1 1. D 2. C 3. D 4. B 5. B 6. C 7. C 8. B 9. B 10. A 11. D 12. D 13. A 14. A 15. C 16. B 17. C 18. D 19. D 20. A 21. B 22. B 23. D 24. D 25. B 26. B 27. B 28. C 29. D 30. D 31. C 32. C 33. C 34. D 35. B 36. C 37. A 38. B 39. D 40. C 41. C 42. D 43. A 44. D 45. D 46. A, B 47. C, D 48. B, C 49. C, D 50. A, B ANSWER KEY ANSWERS EXPLAINED Section I: Multiple-Choice 1. (D) Twice the initial vertical velocity will give twice the time in flight. Average vertical velocity will also be doubled. Displacement is the product of these two: 2 × 2 = 4. Alternatively, one could use v 2 = v 0 2 + 2ad since v at the maximum height is zero. Since v 0 is doubled and then squared, the vertical displacement d must be 4 times bigger. Free-fall problems are independent of mass. 2. (C) Conservation of momentum: P tot = 2(+4) + 5(–1) = +3 kg m/s = mv = (7 kg)v v = +3/7 m/s The collision is inelastic since the carts stick together. 3. (D) Higher altitude is strictly a function of V Y (Projectile Y). Range is a function of both V X and V Y such that the angles equally above and below 45 degrees (the max angle for range) will result in equal horizontal displacement. 30 degrees and 60 degrees are both 15 degrees off from 45 degrees.
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380 AP PHYSICS 1 AND 2
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1. D
2. C
3. D
4. B
5. B
6. C
7. C
8. B
9. B
10. A
11. D
12. D
13. A
14. A
15. C
16. B
17. C
18. D
19. D
20. A
21. B
22. B
23. D
24. D
25. B
26. B
27. B
28. C
29. D
30. D
31. C
32. C
33. C
34. D
35. B
36. C
37. A
38. B
39. D
40. C
41. C
42. D
43. A
44. D
45. D
46. A, B
47. C, D
48. B, C
49. C, D
50. A, B
ANSWER KEY
ANSWERS EXPLAINEDSection I: Multiple-Choice
1. (D) Twice the initial vertical velocity will give twice the time in flight. Average vertical
velocity will also be doubled. Displacement is the product of these two: 2 × 2 = 4.
Alternatively, one could use v2 = v02 + 2ad since v at the maximum height is zero. Since
v0 is doubled and then squared, the vertical displacement d must be 4 times bigger.
Free-fall problems are independent of mass.
2. (C) Conservation of momentum:
Ptot = 2(+4) + 5(–1) = +3 kg m/s = mv = (7 kg)v
v = +3/7 m/s
The collision is inelastic since the carts stick together.
3. (D) Higher altitude is strictly a function of VY (Projectile Y). Range is a function of both
VX and VY such that the angles equally above and below 45 degrees (the max angle for
range) will result in equal horizontal displacement. 30 degrees and 60 degrees are both
15 degrees off from 45 degrees.
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4. (B) Since the 10 N force will start the mass moving, this must be greater than the static
friction force holding the mass in place. The maximum static friction must be 10 N or less.
Fs < 10 N
μN < 10 N
μmg < 10 N
μ(5)(10) < 10
μ < 1/5
5. (B) The object is moving, so the velocity is not zero. The object is not accelerating, so
velocity is constant.
6. (C) In general:
y t y v ty( ) = − −0 021
2g
x(t) = vx0t
Solve for t in the last equation. Then plug back into the first equation and substitute in
y0 = h, vy0 = 0, and vx0 = v0:
y x h x v x v h x v( ) = − ( )( )− ( ) = − ( )012
20 02 2
02g g
7. (C) Maximum acceleration allows you to determine maximum displacement:
ma = kA
Knowing the amplitude allows you to determine easily the maximum speed via energy
conservation:1
2
1
22 2kA mv=
8. (B) Maximum velocities happen when going through the equilibrium point (zero accel-
eration and zero displacement): all KE and no PE.
9. (B) Momentum is conserved during the collision, which enables us to solve for an initial
upward velocity of the combination. Then energy conservation can be used to relate the
height to that initial upward velocity. Choice (A) cannot be used because some unknown
amount of mechanical energy will be lost by the bullet embedding itself in the wood.
10. (A) Constant velocity means no acceleration, so Fnet = 0.
Fpush − Ffriction = 0
Fpush − µkN = Fpush − µkmg = 0
Fpush = µkmg = (0.1)(10 kg)(10 m/s2) = 10 N
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11. (D) First find the acceleration of the system:
Fnet = ma
10 N = (4 + 1 kg)a
a = 2 m/s2
The contact force, P, is the only force felt by the 1 kg mass:
Fnet = ma
P = (1 kg) (2 m/s2) = 2 N
12. (D) P = work/t = FD/t = mgh/t
13. (A) Impulse can be found by Ft if the details of the force are known or, alternatively, by:
Impulse = Δp = (1,500 kg) (0 m/s − 25 m/s) = –37,500 N•s
Ignore the minus sign as the question asks about magnitude.
14. (A) When the block is at the maximum height, static friction is obtained:
Fnet = mg sin θ − µN = 0
mg sin θ − µ(mg cos θ) = 0
µ = (sin θ)/(cos θ) = tan θ
15. (C) Doubling the period requires a quadrupling of length:
T = 2π(l/g)½
16. (B) Impulse = area of F vs T graph = Δp = mvf − 0
Solving for vf = (area under graph)/m
17. (C) Conservation of energy:1
22mv mg h= ∆
1
210 2 25 0 752 2v g h= = ( ) −( )∆ m s m m. .
v = (30)½ = 5.5 m/s
18. (D) Gravitational field strength halfway between any two equal masses is always zero as
each contributes oppositely directed gravitational fields.
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19. (D) Conservation of energy while on the frictionless hills can give the speed at the top
of the hill:
1
22mv mg h= =KE ∆
Then impulse equals change in momentum can be used since the final momentum must
be zero.
20. (A)
Mechanical energy = +mgh mv
1
22
Energy lost or gained“ ” “ ”= + − +
mgH mv mgH mv2 2
21 1
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2
1
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Work by forces other than gravity = change in energy
21. (B) Energy conservation:
1
22kx mgh=
Solving for h :
h = kx 2 /2 mg
Doubling x will quadruple the height, whereas all other factors will only double the
height.
22. (B) Circular motion at the top:
F net = mg + N = mv 2 / r
The lowest speed will be when there is no normal force ( N = 0):
mg = mv 2 / r
v top = ( gr ) ½
KE at the bottom must give both this speed and PE to gain 2 r in height:
E bottom = E top
1
22
1
22 2mv gm r mv= ( )+ top
1
22
1
22mv gm r m gr= ( )+ ( )
Solving for v :
v = (5 gr ) ½
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23. (D) The two 2 Ω resistors are in series with each other: 2 Ω + 2 Ω = 4 Ω.
This 4 Ω equivalent resistance is in parallel with the existing 4 Ω resistor: ¼ Ω + ¼ Ω =
½ Ω. So the equivalent resistance for that section of the circuit is 2 Ω. This 2 Ω equivalent
resistance is in series with the 3 Ω resistor: 2 Ω + 3 Ω = 5 Ω.
24. (D) The 15 volts must be split between the 3-ohm resistor and the 2-ohm equivalent
resistance of the right-hand side (see answer 23). Voltage for the 4-ohm resistor is the
same as the voltage across the 2-ohm equivalent resistance of the right-hand side:
V = (2/5)(15 V) = 6 V
25. (B) The 15-volt battery will supply 3 amps of current for the 5-ohm circuit:
V = IR
15 V = (3A)(5 ohm)
This 3-amp current will split as it comes to the branching point before the 4-ohm resistor.
Since both pathways have equal resistance (4 ohms), the current will split evenly:
1.5 amps.
26. (B) Resistance is determined by:
ρL/A
The same material means the resistivity, ρ, is the same. Letting L → L/2 and A → 2A:
ρL/A → ρ(L/2)/(2A) = (ρL/A)/4
27. (B) The wavelength is set by the length of the standing wave and the number of the
harmonic. Therefore the wavelength remains the same. The frequency of the wave must
have been raised to correspond to the higher wave speed: λf = v.
28. (C) The Doppler effect can be used to determine relative speed toward or away from the
source by looking at frequency shift in the reflected wave. Note that the velocity vector
cannot be determined. Components of velocity not directed toward or away from the
receiver do not contribute to the Doppler shift.
29. (D) The fundamental frequency in a half-pipe is ¼ wavelength:
Wavelength = wave speed/frequency = 340/340 = 1 m
The pipe needs to be ¼ of this: 0.25 m = 25 cm.
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30. (D) Any 45-45-90 triangle has sides of equal length. Therefore, a 45° vector would have
equal length components. So would 135°, 225°, and 315°, as these vectors all form 45-45-
90 triangles with their components.
31. (C) Add the components of the vectors:
A x + B x = –2 + 5 = 3
A y + B y = 3 + 1 = 4
Use the Pythagorean theorem on these net components:
3 2 + 4 2 = 5 2
32. (C) Maximum vector addition is when the two vectors are aligned (0°) and minimum is
when they are opposite (180°). All values in between will steadily decrease the resultant
from maximum to minimum.
33. (C) Maximum range is at 45° since this gives decent time in flight and decent horizontal
velocity.
34. (D) First, find the time in flight:
h t= ( )1
210 2
45 = 5 t 2
t = 3s
Now use this time to find the final speed:
v f = at = (10 m/s 2 )(3 s) = 30 m/s
35. (B) Find time to cross the river using only perpendicular components:
D = V y t
240 = 8 t
t = 30 s
Next find the downstream distance using the parallel component:
D = V x t
D = (6 m/s) (30 s) = 180 m
36. (C) Work is the area under the curve:
(4 N)(6 m) + (2 N)(4 m) = 24 J + 8 J = 32 J
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37. (A ) work = F average · displacement
32 J = ( F average )(10 m)
F average = 3.2 N
38. (B) The bathroom scale reads the normal force:
F net = N − mg = ma
0.5 m/s 2 = 0.05 g
N − mg = m (0.05 g )
N = m (1.05 g )
The reading will be 5% too high.
39. (D) Balanced means the torques are equal and opposite:
50 kg · g · 1.2 = 70 kg · g · x
x = 6/7 = 0.86
40. (C) Both objects start with same potential energy. However, the rolling object must use
some of that potential energy for rotational energy, leaving less for linear kinetic energy.
Therefore, the rolling object moves more slowly down the hill.
41. (C) Universal gravity (and the gravitational field) are 1/ R 2 laws; doubling R will quarter