AP Physics 1: Algebra-Based Unit 7 Practice Test & Exam | 20 Questions

Refer to the figure below.

1. [Skill: 5A | Topic: 7.1] A student measures the horizontal net force on a cart as it is displaced by a distance x from an equilibrium position on a low-friction track. The data are plotted as net force $F_{net}$ versus displacement x. Which graph best represents a cart undergoing simple harmonic motion about x = 0? [Image Cue]: Graph set (four small graphs), Title: "$F_{net}$ vs. x", Axes: horizontal x (m), vertical $F_{net}$ (N). Option A: straight line through origin with negative slope. Option B: straight line through origin with positive slope. Option C: upward-opening parabola through origin ($F_{net} \propto x^2$). Option D: horizontal line ($F_{net}$ constant, nonzero).

(A)A graph that is a straight line through the origin with negative slope(B)A graph that is a straight line through the origin with positive slope(C)A graph that is a parabola opening upward with vertex at the origin(D)A graph that is a horizontal line at a constant positive force

Refer to the figure below.

2. [Skill: 4A | Topic: 7.1] An object moves along the x-axis. The net force on the object depends on its position and is shown in the graph. At what position is the equilibrium position of the system? [Image Cue]: Single graph, Title: "$F_{net}$ vs. x", Axes: x (m) from -3 to +3, $F_{net}$ (N) from -6 to +6. The curve crosses $F_{net}=0$ at x = -2 m and x = +1 m. Near x = +1 m, the curve has a negative slope (crosses from positive $F_{net}$ at slightly smaller x to negative $F_{net}$ at slightly larger x). Near x = -2 m, the curve has a positive slope.

(A)x = -2 m only(B)x = +1 m only(C)Both x = -2 m and x = +1 m(D)Neither; equilibrium requires $F_{net}$ to be maximum

3. [Skill: 1B | Topic: 7.1] A block oscillates back and forth along a frictionless horizontal track about an equilibrium position at x = 0. At a particular instant the block is located at x > 0 (to the right of equilibrium). Which statement correctly describes the direction of the restoring force required for simple harmonic motion? [Image Cue]: Optional diagram of a horizontal line with equilibrium at x=0 and a block shown at a point to the right labeled x>0.

(A)The restoring force is directed to the right because the block is to the right of equilibrium.(B)The restoring force is directed to the left because it must oppose the displacement from equilibrium.(C)The restoring force is zero because the block is momentarily at rest at x > 0.(D)The restoring force can point either left or right depending on the speed of the block.

4. [Skill: 3A | Topic: 7.1] A student claims that any motion that repeats in time (periodic motion) must be simple harmonic motion. Which additional information, if true, would be sufficient to support the student’s claim that the motion is specifically simple harmonic? [Image Cue]: none

(A)The object returns to the same position after a fixed time interval.(B)The object’s speed is greatest when it passes through the middle of its motion.(C)The net force on the object is proportional to its displacement from equilibrium and opposite in direction.(D)The object moves back and forth between two turning points.

5. [Skill: 2A | Topic: 7.1] A student displaces an object from equilibrium along a line and measures the net force acting on it. The measurements are: - When $x = +0.10\ \text{m}$, $F_{net} = -0.50\ \text{N}$ - When $x = -0.10\ \text{m}$, $F_{net} = +0.50\ \text{N}$ Assuming these data are representative of the force for other small displacements, which relationship best models the net force as a function of x? [Image Cue]: none

(A)$F_{net} = (5.0\ \text{N/m})x$(B)$F_{net} = (-5.0\ \text{N/m})x$(C)$F_{net} = (0.20\ \text{N}\cdot\text{m})/x$(D)$F_{net} = -0.50\ \text{N}$ (constant)

Refer to the figure below.

6. [Skill: 5A | Topic: 7.2] [Image Cue]: Displacement–time graph, "Mass on a Spring: x vs t", horizontal axis labeled time t (s) from 0 to 6 s, vertical axis labeled displacement x (m). The curve is sinusoidal and completes exactly 3 full cycles between t = 0 s and t = 6 s. A mass oscillates in simple harmonic motion as shown. Based on the graph, what is the frequency of the motion?

(A)0.25 Hz(B)0.50 Hz(C)2.0 Hz(D)3.0 Hz

7. [Skill: 2A | Topic: 7.2] Two ideal mass–spring oscillators are set up on a frictionless horizontal surface. System A: mass $m_A = 0.50\,\text{kg}$ attached to a spring with constant $k_A = 200\,\text{N/m}$ System B: mass $m_B = 2.0\,\text{kg}$ attached to a spring with constant $k_B = 200\,\text{N/m}$ What is the ratio of the periods, $\dfrac{T_B}{T_A}$?

(A)0.50(B)1.0(C)2.0(D)4.0

8. [Skill: 5B | Topic: 7.2] A student investigates the period of a mass–spring system by attaching different masses to the same ideal spring and measuring the period $T$. Data: - $m = 0.10\,\text{kg}$, $T = 0.44\,\text{s}$ - $m = 0.20\,\text{kg}$, $T = 0.63\,\text{s}$ - $m = 0.30\,\text{kg}$, $T = 0.77\,\text{s}$ Assuming the system behaves as an ideal mass–spring oscillator, what is the best estimate of the spring constant $k$?

(A)5 N/m(B)10 N/m(C)20 N/m(D)40 N/m

9. [Skill: 2B | Topic: 7.2] Two simple pendulums swing with small amplitude at the same location. Pendulum 1 has length $L_1 = 0.25\,\text{m}$. Pendulum 2 has length $L_2 = 1.00\,\text{m}$. What is the ratio of their periods, $\dfrac{T_2}{T_1}$?

(A)0.50(B)2.0(C)4.0(D)16

10. [Skill: 2A | Topic: 7.2] A simple pendulum of length $L = 0.90\,\text{m}$ oscillates with a measured period of $T = 1.9\,\text{s}$ for small angles. Based on these measurements, what is the best estimate of the local gravitational field strength $g$?

(A)2.5 m/s^2(B)4.9 m/s^2(C)9.8 m/s^2(D)19.6 m/s^2

Refer to the figure below.

11. **1. [Skill: 1.C | Topic: 7.3]** A mass on a spring oscillates on a frictionless horizontal surface. A graph of displacement $x$ versus time $t$ is shown. Which of the following equations best represents the motion shown in the graph?

(A)$x=0.20\cos(\pi t)$(B)$x=0.20\sin(\pi t)$(C)$x=0.20\cos(2\pi t)$(D)$x=0.20\sin(2\pi t)$

12. **2. [Skill: 6.A | Topic: 7.3]** A student investigates whether changing the amplitude affects the period of a mass-spring oscillator on a frictionless surface. Trial 1: The student pulls the mass to an amplitude of 0.10 m and measures a period of 1.6 s. Trial 2: The student pulls the same mass to an amplitude of 0.20 m and releases it from rest. Which of the following best predicts the period measured in Trial 2?

(A)0.80 s, because doubling amplitude halves the period(B)1.6 s, because the period is independent of amplitude for SHM(C)3.2 s, because doubling amplitude doubles the period(D)It cannot be predicted without knowing the mass and spring constant

13. **3. [Skill: 1.B | Topic: 7.3]** A block attached to a spring oscillates in SHM on a frictionless surface. At a particular instant, the block is to the right of equilibrium ($x>0$) and moving to the left (its displacement is decreasing). Which of the following correctly describes the signs of the block’s velocity $v$ and acceleration $a$ at that instant?

(A)$v>0$ and $a>0$(B)$v>0$ and $a<0$(C)$v<0$ and $a>0$(D)$v<0$ and $a<0$

Refer to the figure below.

14. **4. [Skill: 2.B | Topic: 7.3]** A displacement-versus-time graph for an object in SHM is shown. Which of the following equations best represents the motion shown in the graph?

(A)$x=0.30\sin(2\pi t)$(B)$x=0.30\cos(2\pi t)$(C)$x=0.30\sin(4\pi t)$(D)$x=0.30\cos(4\pi t)$

15. [Skill: 4.A | Topic: 7.4] A student investigates a block–spring oscillator on a frictionless horizontal surface. The block has mass 0.50 kg and is attached to a spring with spring constant 200 N/m. The block is pulled to an amplitude of 0.10 m and released from rest. At several instants, the student records the block’s position x (measured from equilibrium) and speed v. Which recorded data point is inconsistent with an ideal SHM model because it violates conservation of mechanical energy? Data points: 1) x = 0.00 m, v = 2.0 m/s 2) x = 0.06 m, v = 1.6 m/s 3) x = 0.08 m, v = 1.0 m/s 4) x = 0.10 m, v = 0.0 m/s

(A)Data point 1(B)Data point 2(C)Data point 3(D)Data point 4

16. [Skill: 2.A | Topic: 7.4] A block of mass 0.40 kg oscillates on a frictionless surface attached to a spring with spring constant 50 N/m. The amplitude of the motion is 0.20 m. What is the speed of the block when its displacement from equilibrium is 0.12 m?

(A)0.90 m/s(B)1.3 m/s(C)1.8 m/s(D)2.2 m/s

17. [Skill: 1.B | Topic: 7.4] A mass on a spring undergoes simple harmonic motion with amplitude $A$. Three positions are labeled along the x-axis (x measured from equilibrium): P: $x=-A$ Q: $x=-\tfrac{A}{2}$ R: $x=0$ In an ideal oscillator, which ranking of the kinetic energy at the three positions is correct?

(A)$K_P > K_Q > K_R$(B)$K_R > K_Q > K_P$(C)$K_Q > K_R > K_P$(D)$K_P = K_Q = K_R$

Refer to the figure below.

18. [Skill: 4.B | Topic: 7.4] A block–spring oscillator moves on a frictionless horizontal surface. At some instant during the motion, an energy bar chart for the block–spring system shows kinetic energy 0.75 J and spring potential energy 0.25 J. The spring constant is 100 N/m. Based on the chart, what is the amplitude of the oscillation?

(A)0.071 m(B)0.10 m(C)0.14 m(D)0.20 m

AP Physics 1: Algebra-Based Unit 7: Oscillations Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

B. Short Answer Questions (2 Questions)

AP Physics 1: Algebra-Based Unit 7: Oscillations Practice Exam

Exam Details

A. Multiple-Choice Questions (18 Questions)

B. Short Answer Questions (2 Questions)