Practice Final Exam
1. A cylinder with a piston contains x₁ liters of an ideal diatomic gas at x₂ atm and x₃ K. The gas is subject to an adiabatic compression from its initial volume to 1/N its initial volume. What is the temperature after the compression? N, x₁, x₂, and x₃ are some numbers.
2. A pianist considers two strings in the piano that are side-by-side. Their construction is identical in terms of their linear mass density and tension—only the length is different. If, when the strings are vibrating in their fundamental modes, a beat frequency of x₁ Hz is heard, and if the average frequency heard is x₂ Hz, what is the ratio of lengths of the higher frequency to lower frequency string? x₁ and x₂ are some numbers.
3. An explosion is detected x₁ m away from ground-zero, where the intensity is recorded to be x₂×10⁹ W/m². About 5 s later, the sound wave is recorded x₃ km away from ground-zero. What will its intensity by at that distance? (We ignore absorption losses in this calculation! x₁, x₂, and x₃ are some numbers.)
4. A mass that can oscillate without friction on a horizontal surface is attached to a horizontal spring and is pulled to the right and is released from rest. The period of the oscillation is x₁ s. The speed of the mass is x₂ m/s at t = x₃ s. What is the amplitude of the oscillation? (x₁, x₂, and x₃ are some numbers.)
5. A mass m₁ = x₁ kg is at rest on a frictionless horizontal surface and connected to a wall by an ideal spring with a spring constant of k = x₂ N/m as shown in the figure. A second mass m₂ = x₃ kg is moving to the left at v₀ = x₄ m/s. The two masses then collide perfectly inelastically. What is the maximum compression of the spring? (x₁, x₂, x₃, and x₄ are some numbers.)
6. A thin uniform rod (length = x₁ cm, mass = x₂ kg) is pivoted about a horizontal frictionless pin through one end of the rod. The moment of inertia of the rod through this axis is (1/3) mL². The rod is released when it is below the horizontal and it makes the angle θ with the horizontal. If the angular acceleration of the rod at the instant it is released is x₃ rad/s², what is the angle θ? (x₁, x₂, and x₃ are some numbers.)
7. A uniform solid sphere of mass M and radius R is rolling without slipping along a level plane when it encounters a ramp that is at an angle of θ = x₁ degree above horizontal. The maximum distance that the sphere rolls without slipping up the ramp before (instantaneously) stopping and rolling back down is x₃ m. What was the linear speed of the sphere before it encountered the ramp? (x₁, x₂, and x₃ are some numbers.)
8. A turntable is initially at rest. It starts rotating with a constant angular acceleration for a period of x₁ seconds. It then starts to slow down with an angular acceleration of - x₂ rad/s² for another x₁ seconds. Totally turntable made x₃ rotations. What is the maximum angular acceleration the turntable reaches? (x₁, x₂, and x₃ are some numbers.)
9. A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L. If the mass is pulled back so that it is raised an amount L/4 and then released, what is the tension on the string at the bottom of the swing?
10. Particle one of mass m initially moves to the right at v. Particle two of mass 4m is initially at rest. After they undergo an elastic collision, particle one moves directly down. What is the final speed of particle one?
11. A x₁-kg child starts from rest at the top of a slide inclined at x₂° relative to the horizontal. The slide is x₃ m long. The coefficient of the kinetic friction of the slide is x₄. When reaching the bottom of the slide, the child's speed is: (x₁, x₂, x₃, and x₄ are some numbers.)
12. A mass, m₁ slides on a frictionless surface. This mass is connected to another mass m₂ of x₁ kg by a massless string over a frictionless pulley. The masses are held motionless and then released. Mass m₂ accelerates downward at x₂ m/s². What is the mass of m1? (x₁ and x₂ are some numbers.)
13. An object is launched up a x₁ degree slope at an angle of x₂ degrees above the incline of the slope and lands a distance of x₃ m up the slope. What is the object's initial speed? (x₁, x₂, and x₃ are some numbers.)
14. A car moving along the x direction has acceleration, ax that varies with time as shown in the figure. At the moment, t = 0 s, the car is located at x = 12 m and has a velocity of 6 m/s in the positive x direction. What is the velocity of the car at t = 4.0 s?
15. If you head at a compass heading of x₁° for x₂ m, then go on a heading of x₃° for x₄ m, how far are you from your starting point? (x₁, x₂, x₃, and x₄ are some numbers.)
16. A sphere and a cube have the same volume. If the radius of the sphere is x₁ cm, then what is the area of one side of the cube?
1. A cylinder with a piston contains x₁ liters of an ideal diatomic gas at x₂ atm and x₃ K. The gas is subject to an adiabatic compression from its initial volume to 1/N its initial volume. What is the temperature after the compression? N, x₁, x₂, and x₃ are some numbers.
2. A pianist considers two strings in the piano that are side-by-side. Their construction is identical in terms of their linear mass density and tension—only the length is different. If, when the strings are vibrating in their fundamental modes, a beat frequency of x₁ Hz is heard, and if the average frequency heard is x₂ Hz, what is the ratio of lengths of the higher frequency to lower frequency string? x₁ and x₂ are some numbers.
3. An explosion is detected x₁ m away from ground-zero, where the intensity is recorded to be x₂×10⁹ W/m². About 5 s later, the sound wave is recorded x₃ km away from ground-zero. What will its intensity by at that distance? (We ignore absorption losses in this calculation! x₁, x₂, and x₃ are some numbers.)
4. A mass that can oscillate without friction on a horizontal surface is attached to a horizontal spring and is pulled to the right and is released from rest. The period of the oscillation is x₁ s. The speed of the mass is x₂ m/s at t = x₃ s. What is the amplitude of the oscillation? (x₁, x₂, and x₃ are some numbers.)
5. A mass m₁ = x₁ kg is at rest on a frictionless horizontal surface and connected to a wall by an ideal spring with a spring constant of k = x₂ N/m as shown in the figure. A second mass m₂ = x₃ kg is moving to the left at v₀ = x₄ m/s. The two masses then collide perfectly inelastically. What is the maximum compression of the spring? (x₁, x₂, x₃, and x₄ are some numbers.)
6. A thin uniform rod (length = x₁ cm, mass = x₂ kg) is pivoted about a horizontal frictionless pin through one end of the rod. The moment of inertia of the rod through this axis is (1/3) mL². The rod is released when it is below the horizontal and it makes the angle θ with the horizontal. If the angular acceleration of the rod at the instant it is released is x₃ rad/s², what is the angle θ? (x₁, x₂, and x₃ are some numbers.)
7. A uniform solid sphere of mass M and radius R is rolling without slipping along a level plane when it encounters a ramp that is at an angle of θ = x₁ degree above horizontal. The maximum distance that the sphere rolls without slipping up the ramp before (instantaneously) stopping and rolling back down is x₃ m. What was the linear speed of the sphere before it encountered the ramp? (x₁, x₂, and x₃ are some numbers.)
8. A turntable is initially at rest. It starts rotating with a constant angular acceleration for a period of x₁ seconds. It then starts to slow down with an angular acceleration of - x₂ rad/s² for another x₁ seconds. Totally turntable made x₃ rotations. What is the maximum angular acceleration the turntable reaches? (x₁, x₂, and x₃ are some numbers.)
9. A pendulum is composed of a mass m suspended from the ceiling by a massless string of length L. If the mass is pulled back so that it is raised an amount L/4 and then released, what is the tension on the string at the bottom of the swing?
10. Particle one of mass m initially moves to the right at v. Particle two of mass 4m is initially at rest. After they undergo an elastic collision, particle one moves directly down. What is the final speed of particle one?
11. A x₁-kg child starts from rest at the top of a slide inclined at x₂° relative to the horizontal. The slide is x₃ m long. The coefficient of the kinetic friction of the slide is x₄. When reaching the bottom of the slide, the child's speed is: (x₁, x₂, x₃, and x₄ are some numbers.)
12. A mass, m₁ slides on a frictionless surface. This mass is connected to another mass m₂ of x₁ kg by a massless string over a frictionless pulley. The masses are held motionless and then released. Mass m₂ accelerates downward at x₂ m/s². What is the mass of m1? (x₁ and x₂ are some numbers.)
13. An object is launched up a x₁ degree slope at an angle of x₂ degrees above the incline of the slope and lands a distance of x₃ m up the slope. What is the object's initial speed? (x₁, x₂, and x₃ are some numbers.)
14. A car moving along the x direction has acceleration, ax that varies with time as shown in the figure. At the moment, t = 0 s, the car is located at x = 12 m and has a velocity of 6 m/s in the positive x direction. What is the velocity of the car at t = 4.0 s?
15. If you head at a compass heading of x₁° for x₂ m, then go on a heading of x₃° for x₄ m, how far are you from your starting point? (x₁, x₂, x₃, and x₄ are some numbers.)
16. A sphere and a cube have the same volume. If the radius of the sphere is x₁ cm, then what is the area of one side of the cube?
