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Inclined Planes quiz #1

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  • How does the time it takes for a box to reach the bottom of a frictionless incline compare to the time for a disk, and what factors influence this difference?
    On a frictionless incline, a box (modeled as a block) and a disk will reach the bottom at different times if rotational inertia is considered. The box, which does not rotate, accelerates faster (a = g sin θ) than the disk, which must also rotate and thus has less acceleration. Therefore, the box reaches the bottom sooner than the disk because it has a greater acceleration down the incline.
  • What is the maximum angle of an incline at which a car can be parked without sliding, assuming no friction?
    If there is no friction, a car cannot be parked on any incline without sliding; it will always accelerate down the slope. In real situations, the maximum angle depends on the coefficient of static friction, but for a frictionless incline, the maximum angle is zero.
  • What is the difference between a wedge and an inclined plane in terms of their physical function?
    A wedge is a movable inclined plane used to separate or lift objects by applying force, while an inclined plane is a stationary surface set at an angle to help move objects up or down by reducing the required force.
  • When walking up an inclined plane, what is the resistance force you must overcome?
    The resistance force when walking up an inclined plane is the component of your weight acting parallel to the incline, which is mg sin θ, where m is your mass and θ is the angle of the incline.
  • As a block slides down a frictionless incline, what forces act on it and how do they affect its motion?
    As a block slides down a frictionless incline, the forces acting on it are gravity (mg) and the normal force. Gravity is decomposed into two components: mg sin θ (parallel to the incline, causing acceleration) and mg cos θ (perpendicular to the incline, balanced by the normal force). The block accelerates down the incline with a = g sin θ.
  • If a cat runs up an incline, what is her speed at the top in terms of her initial speed and the incline's properties?
    The cat's speed at the top of the incline depends on her initial speed, the angle of the incline, and the effects of gravity. If the incline is frictionless and only gravity acts, her speed at the top can be found using energy conservation or kinematics, accounting for the loss in kinetic energy due to the gain in potential energy.
  • What should you do to maintain a constant speed while driving up a steep incline?
    To maintain a constant speed while driving up a steep incline, you must apply enough force to counteract the component of gravity pulling you down the slope (mg sin θ), typically by increasing engine power or throttle.
  • What is the acceleration of a ball on an inclined plane when the plane is raised to be vertical?
    When the inclined plane is vertical (θ = 90°), the acceleration of the ball is g sin 90° = g, which is the acceleration due to gravity.
  • Why is the mechanical advantage of an inclined plane less than that of a lever?
    The mechanical advantage of an inclined plane can be less than that of a lever because the inclined plane requires a longer path to move the object, and in practical cases, friction and other losses reduce its efficiency compared to the lever.
  • How can you determine the angle at which a wire meets the ground if it is laid along an inclined plane?
    The angle at which a wire meets the ground when laid along an inclined plane is equal to the angle of the incline, θ, relative to the horizontal.
  • What is a disadvantage of using an inclined plane to lift a heavy object?
    A disadvantage of using an inclined plane to lift a heavy object is that it requires moving the object over a longer distance, and in real situations, friction can make the process less efficient.
  • When operating a forklift with a full load up an incline, what should you do to ensure safety and control?
    When operating a forklift with a full load up an incline, you should apply enough force to counteract the gravitational component pulling the load down the slope (mg sin θ) and maintain a controlled, constant speed.
  • How do you calculate the force required to drive a 3000 lb load down a ramp with a 15 percent grade?
    To calculate the force required to drive a 3000 lb load down a ramp with a 15 percent grade, find the angle θ corresponding to the grade, then compute the parallel component of weight: F = mg sin θ, where m is the mass and g is gravity.
  • What is the recommended driving technique when going up a steep incline?
    When driving up a steep incline, you should maintain a constant speed by applying enough force to overcome the component of gravity acting down the slope (mg sin θ).
  • What is the acceleration of a 10 kg block sliding down a smooth inclined surface?
    The acceleration of a 10 kg block sliding down a smooth (frictionless) inclined surface is a = g sin θ, where g is the acceleration due to gravity and θ is the angle of the incline.
  • What is the acceleration of a block sliding down a frictionless inclined ramp?
    The acceleration of a block sliding down a frictionless inclined ramp is a = g sin θ, where g is the acceleration due to gravity and θ is the angle of the incline.