Friction and Drag Quiz
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What is the coefficient of static friction if a 51 kg crate requires a 230 N force to start moving?

  • 0.67
  • 0.56 (correct)
  • 0.45
  • 0.75

    • What is the coefficient of kinetic friction if a 51 kg crate is kept moving at constant velocity with a force of 200 N?

  • 0.35
  • 0.40 (correct)
  • 0.25
  • 0.45

    • When a horizontal force of 50 N is applied to a 51 kg crate at rest, what is the friction force?

  • 50 N
  • 230 N
  • 0 N (correct)
  • 200 N

    • At what tilt angle does a 95.0 kg crate begin to slide down a truck's bed if the coefficient of kinetic friction is 0.40?

    <p>23.3°</p> Signup and view all the answers

    What is the normal force acting on a toboggan sliding down a hill with no friction?

    <p>$mg imes ext{cos}( heta)$</p> Signup and view all the answers

    If the angle of the slope is known along with $m$ and $ u_k$, how can one express the angle made by a toboggan moving with constant velocity?

    <p>In terms of both mass and friction coefficient</p> Signup and view all the answers

    What is the expression for acceleration of a toboggan on a slope with friction?

    <p>$a = g imes ext{sin}( heta) - u_k$</p> Signup and view all the answers

    What will happen to a toboggan's acceleration as the coefficient of kinetic friction increases on a hill?

    <p>Acceleration decreases</p> Signup and view all the answers

    What is the force of gravity between two point objects, such as apples, if they are separated by 13.2 cm?

    <p>It can be calculated using the formula $F = G \frac{m_1 m_2}{r^2}$.</p> Signup and view all the answers

    What is the combined gravitational force on star A by stars B and C, given their masses?

    <p>It can be calculated using their masses and distances from A.</p> Signup and view all the answers

    How does the acceleration due to gravity on the Moon compare to that on Earth?

    <p>It is less than the Earth's acceleration due to gravity.</p> Signup and view all the answers

    What would be the expected weight of a 225 kg lunar rover on Earth compared to its weight on the Moon?

    <p>It would weigh less on the Moon due to lower gravity.</p> Signup and view all the answers

    What can be inferred about the mass of Mars based on the acceleration calculated for a falling rock?

    <p>It must be smaller than that of Earth but greater than that of the Moon.</p> Signup and view all the answers

    What is the angular velocity in rad/s of a wind turbine rotating at 17.0 rpm?

    <p>6.35 rad/s</p> Signup and view all the answers

    What is the angular velocity of a CD rotating through 106° in 0.0860 seconds expressed in rad/s?

    <p>12.4 rad/s</p> Signup and view all the answers

    If a centrifuge creates a linear speed of 90.6 m/s at a distance of 9.25 cm from the axis of rotation, what is the centripetal acceleration?

    <p>1222.46 m/s²</p> Signup and view all the answers

    What is the maximum speed a 1200 kg car can maintain on a turn with a radius of 45 m and a coefficient of static friction of 0.82 without skidding?

    <p>24.35 m/s</p> Signup and view all the answers

    What is the appropriate banking angle for a car traveling at 20.5 m/s in a turn of radius 85.0 m?

    <p>26.57°</p> Signup and view all the answers

    When a person is seated at the top of a Ferris wheel, what influences the force the seat exerts on the passenger?

    <p>Normal force and gravitational force</p> Signup and view all the answers

    What is the normal force exerted on a motorcycle when it drives around a vertical track at a speed v?

    <p>Depends on the mass and speed of the motorcycle</p> Signup and view all the answers

    What expression defines the centripetal acceleration of a pendulum bob moving in a horizontal circle at constant speed?

    <p>$a_c = \frac{v^2}{L}$</p> Signup and view all the answers

    What is the work done by the applied force when lifting a 4.10 kg box to a height of 1.60 m with a force of 52.7 N?

    <p>82.32 J</p> Signup and view all the answers

    How do you calculate the kinetic energy of a 0.15 kg baseball moving at a speed of 36 m/s just before it is caught?

    <p>$ rac{1}{2} mv^2 = 108 J$</p> Signup and view all the answers

    What is the potential energy of a 55-kg skateboarder at the maximum height reached if the height is 7 m?

    <p>529.2 J</p> Signup and view all the answers

    What is the work done on the spring when compressed by 1.0 cm, given that its spring constant is 600 N/m?

    <p>0.03 J</p> Signup and view all the answers

    What is the effect of the coefficient of kinetic friction of 0.16 on the work done by the ground on a sled being pulled at a constant speed?

    <p>Does not affect the total work done</p> Signup and view all the answers

    If a 1.70-kg block compresses a spring with a constant of 955 N/m a distance of 4.60 cm, what is its initial kinetic energy?

    <p>2.94 J</p> Signup and view all the answers

    How much work is done by Diane when pulling a sled a distance of 120 m against friction?

    <p>3900 J</p> Signup and view all the answers

    What represents the change in mechanical energy when the 350 kg roller coaster car descends without friction?

    <p>Potential energy decreases while kinetic energy increases</p> Signup and view all the answers

    What is the relationship between the work done by the water resistance and the kinetic energy of the diver as he descends into the water?

    <p>The work done is equal to the loss of kinetic energy.</p> Signup and view all the answers

    What is the spring potential energy stored in a compressed spring if its force constant is 730 N/m and it is compressed by 0.05 m?

    <p>1.83 J</p> Signup and view all the answers

    How does the work done by non-conservative forces affect the total mechanical energy of the jogger running uphill?

    <p>It decreases the total mechanical energy.</p> Signup and view all the answers

    What is the maximum potential energy of a 1.75-kg block at the top of a ramp of height h when it is released and slides down?

    <p>$14.70 J$</p> Signup and view all the answers

    What speed will the 2.40 kg block achieve just before the second block lands if it descends a distance of 0.500 m?

    <p>3.92 m/s</p> Signup and view all the answers

    If a car accelerates from 13.4 m/s to 17.9 m/s in 3.00 seconds, what is the required work done on the car to achieve this speed change?

    <p>2160 J</p> Signup and view all the answers

    What factors influence the height to which a block can rise after being released from a compressed spring?

    <p>The mass of the block and the spring constant.</p> Signup and view all the answers

    What energy transformation occurs when a block slides down a frictionless ramp and then across a rough patch?

    <p>Potential energy converts to kinetic energy, then partially to thermal energy.</p> Signup and view all the answers

    Study Notes

    Friction and Drag

    • Friction: A force that opposes motion between two surfaces in contact.
    • Static Friction: Friction that prevents an object from moving when a force is applied.
    • Kinetic Friction: Friction that acts on a moving object.
    • Coefficient of Static Friction (μs): The ratio of the maximum static friction force to the normal force.
    • Coefficient of Kinetic Friction (μk): The ratio of the kinetic friction force to the normal force.
    • Drag: A type of friction that opposes the motion of an object through a fluid (like air or water).

    Examples

    • Moving a Crate: Calculating the coefficient of static and kinetic friction when moving a crate across a floor.
    • Tilted Truck Bed: Finding the coefficient of static friction and the acceleration of a crate sliding down a tilted truck bed.
    • Toboggan on a Hill: Determining the normal force and acceleration of a toboggan on a snow-covered hill with and without friction.

    Key Concepts

    • Normal Force: The force exerted by a surface perpendicular to the object in contact.
    • Net Force: The vector sum of all forces acting on an object.
    • Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
    • Equilibrium: When the net force on an object is zero and the object is at rest or moving with a constant velocity.
    • Constant Velocity: Occurs when the net force acting on an object is zero.

    Applying Newton's Laws

    • Free-Body Diagram: A visual representation of all the forces acting on an object.
    • Newton's Second Law: Used to solve for the acceleration of an object.
    • Trigonometry: Used to resolve forces into their components.
    • Friction Forces: Always act in the opposite direction of motion or impending motion.
    • Drag Forces: Increase with the speed of the object.

    Uniform Circular Motion

    • Angular Velocity: A rotating object's angular velocity (ω) is the rate at which its angular position changes over time. It's measured in radians per second (rad/s).
    • Relationship between Angular Velocity and Period: The period (T) of a rotating object is the time it takes for one complete revolution. The relationship between angular velocity and period is: ω = 2π/T.
    • Centripetal Acceleration: An object moving in a circle experiences a centripetal acceleration (acp) directed towards the center of the circle. Its magnitude is given by: acp = v²/r = ω²r, where v is the object's speed and r is the radius of the circle.
    • Centripetal Force: The force causing the centripetal acceleration is called the centripetal force. It is given by: Fc = macp = mv²/r = mω²r, where 'm' is the object's mass.

    Banking of Roads

    • Banking Angle: A road banked at an angle θ allows vehicles to safely navigate curves without relying solely on friction.
    • Angle Calculation: The optimal banking angle for a given speed (v) and curve radius (r) can be calculated using: tanθ = v²/gr, where 'g' is the acceleration due to gravity.

    Conical Pendulum

    • Conical Pendulum: A conical pendulum consists of a mass (m) attached to a string of length (L) that swings in a horizontal circle.
    • Tension and Centripetal Force: The tension (T) in the string provides the centripetal force for the circular motion.
    • Angle and Velocity: The angle (β) the string makes with the vertical and the angular velocity (ω) of the bob are related through: cosβ = g/ω²L.

    Gravity

    • Newton's Law of Universal Gravitation: The force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This is expressed by the equation: F = Gm₁m₂/r², where 'G' is the gravitational constant (6.674 × 10⁻¹¹ N m²/kg²).
    • Acceleration Due to Gravity: The acceleration due to gravity (g) is the acceleration experienced by an object near the surface of a planet or other celestial body. On Earth, g is approximately 9.81 m/s².
    • Acceleration Due to Gravity at Altitude: As you move away from the Earth's surface, the acceleration due to gravity decreases. This can be calculated using: g' = g(R/(R + h))², where 'g' is the acceleration due to gravity at the surface, 'R' is the Earth's radius, and 'h' is the altitude.

    Orbital Motion

    • Orbital Speed: An object orbiting another object has an orbital speed (v) that depends on its distance (r) from the center of the object it orbits.
    • Orbital Period: The time it takes for an object to complete one orbit is called its period (T).
    • Relationship between Orbital Speed, Period, and Distance: The relationship between these quantities is: v = 2πr/T and T² = (4π²/GM)r³, where 'M' is the mass of the object it orbits.

    Work, Energy, and Energy Resources

    • Work is done when a force causes a displacement.
    • Work-energy theorem: The work done on an object is equal to the change in its kinetic energy.
    • Power is the rate at which work is done.

    Work Done by a Force

    • Work done by a constant force: W = Fd cos θ, where W is work, F is force, d is displacement, and θ is the angle between the force and displacement vectors.

    Potential Energy

    • Gravitational potential energy: U = mgh, where U is potential energy, m is mass, g is acceleration due to gravity, and h is height.
    • Elastic potential energy: U = (1/2)kx², where U is potential energy, k is the spring constant, and x is the displacement from equilibrium.

    Conservation of Mechanical Energy

    • Conservation of mechanical energy: In a system where only conservative forces act, the total mechanical energy (sum of kinetic and potential energy) remains constant.
    • Non-conservative forces: Forces like friction, air resistance, and tension can do work that changes the total mechanical energy of a system.

    Power

    • Power: P = W/t, where P is power, W is work, and t is time.
    • Power in terms of force and velocity: P = Fv, where P is power, F is force, and v is velocity.

    Example Problems

    • Lifting a box:
      • The work done by the applied force is positive since it acts in the direction of displacement.
      • The work done by gravity is negative since it acts in the opposite direction of displacement.
    • Pulling a sled:
      • Work done by Diane depends on the horizontal component of her force.
      • Work done by the ground is due to friction and is negative because it opposes the motion of the sled.
    • Compressing a spring:
      • The force constant of a spring relates the force needed to compress it to the compression distance.
      • Work done on the spring is equal to the change in its potential energy.
    • Catching a baseball:
      • The kinetic energy of the ball before being caught depends on its speed.
      • The ball's speed before being caught can be calculated using the conservation of energy.
    • Rollercoaster:
      • The speed of the rollercoaster at the bottom of the loop can be determined by the conservation of energy.
      • The force the rollercoaster exerts on the track is equal to the sum of its weight and the centripetal force required for circular motion.
    • Skateboarding:
      • Conservation of energy allows for calculating the height of the ramp based on the skateboarder's initial and final speeds.
      • The maximum height the skateboarder reaches can be found by equating the initial kinetic energy to the potential energy at the maximum height.
    • Block-spring system:
      • The initial speed of the block can be derived using the conservation of energy and the potential energy stored in the spring.
      • The speed of the block when the spring returns to its equilibrium position can be calculated by equating the potential energy to the kinetic energy.
      • The maximum height reached by the block can be determined by setting the initial potential energy to the final potential energy.
    • Diver in a pool:
      • The work done by the water resistance is negative because it opposes the diver's motion.
    • Jogger running uphill:
      • The work done by the jogger, air resistance, and gravity changes the jogger's kinetic energy.
      • The height of the hill can be calculated using the work-energy theorem.
    • Blocks connected by a string:
      • The speed of the blocks just before the second block hits the floor can be determined using the conservation of energy and accounting for work done by friction.
    • Block sliding down a ramp:
      • The height of the ramp required for the block to reach a specific speed at the bottom can be calculated using the conservation of energy.
    • Block released from a spring:
      • The compression distance of the spring needed for the block to reach a specific speed after crossing a rough patch can be calculated using the conservation of energy.
    • Car accelerating:
      • The minimum power required to accelerate the car is determined by the work needed to increase the car's kinetic energy over a specific time.
    • Jet engine power:
      • The power developed by each jet engine can be calculated using the force produced and the speed of the aircraft.

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    Description

    Test your understanding of friction and drag with this quiz. Explore key concepts such as static and kinetic friction, as well as real-world examples like moving crates and toboggans. Challenge yourself to calculate coefficients and analyze forces at play.

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