MIDTERM 2 PRACTICE

Example Problems from Phys101 Lectures 25 (Fall 2011 Midterm #2)

Problem 1: Torque on a Door

• Setup: Two equal forces applied to a door:

  • First force: at midpoint

  • Second force: at doorknob

• Question: Which force exerts the greater torque?

  • Options:

    • A) the first at the midpoint

    • B) the second at the doorknob

    • C) both exert equal non-zero torques

    • D) both exert zero torques

    • E) additional information is needed

• Answer: B) the second at the doorknob

Problem 2: Rolling Objects on an Incline

• Setup: A disk, a hoop, and a solid sphere released simultaneously on an inclined plane, all rolling without slipping.

• Question: In what order do they reach the bottom?

  • Options:

    • A) disk, hoop, sphere

    • B) hoop, sphere, disk

    • C) sphere, hoop, disk

    • D) hoop, disk, sphere

    • E) sphere, disk, hoop

• Answer: E) sphere, disk, hoop

Problem 3: Figure Skater's Angular Speed

• Setup: A figure skater spins slowly with arms outstretched and brings her arms in close, causing an increase in angular speed.

• Question: This speed increase demonstrates:

  • Options:

    • A) conservation of kinetic energy

    • B) conservation of total energy

    • C) Newton's second law for rotational motion

    • D) conservation of angular momentum

    • E) unrelated to mechanics

• Answer: D) conservation of angular momentum

Problem 4: Balancing a Rod with a Weight

• Setup: A 1-kg ball is hung on a 1-m long rod, balancing at 0.25 m from the weight.

• Question: What is the mass of the rod?

  • Options:

    • A) 0.25 kg

    • B) 0.50 kg

    • C) 1 kg

    • D) 2 kg

    • E) 4 kg

• Answer: C) 1 kg

Problem 5: Moment of Inertia Comparison

• Setup: Two spherical balls made of the same material: Ball A (radius R) and Ball B (radius 2R). Ram = I (moment of inertia of Ball A).

• Question: What is the moment of inertia of Ball B?

  • Options:

    • A) 2I

    • B) 4I

    • C) 8I

    • D) 16I

    • E) 32I

• Answer: E) 32I

Problem 6: Young's Modulus Comparison

• Setup: A uniform steel wire cut into two pieces: 2.0 m and 20 m long. Young's modulus of the first piece is Y.

• Question: Young's modulus of the second piece?

  • Options:

    • A) 0.01Y

    • B) 0.1Y

    • C) Y

    • D) 10Y

    • E) 100Y

• Answer: Not required.

Problem 7: Effect of Steel Chunk on Water Level

• Setup: A boat with a large chunk of steel floating in a lake; the chunk is thrown overboard and sinks.

• Question: What happens to the water level in the lake?

  • Options:

    • A) drops

    • B) rises

    • C) remains the same

    • D) depends on the size of the steel

    • E) insufficient information

• Answer: A) drops

Problem 8: Torque Calculation with Triceps Muscle

• Setup: Forearm accelerating a 5.0 kg ball at 4.0 m/s² using the triceps muscle.

• Tasks:

  • (a) Calculate the torque needed.

  • (b) Calculate the force exerted by the triceps muscle.

Problem 9: Uniform Beam in Horizontal Position

• Setup: A 2.00 m long beam with mass 5.00 kg, supported horizontally by a cable at an angle of 25.0°.

• Tasks:

  • (a) Find the tension in the cable.

  • (b) Find the angular acceleration if the cable snaps.

  • (c) Find the angular speed when the beam hits the wall.

Problem 10: Rotating Platform with Student Walking Inward

• Setup: A horizontal rotating platform with radius 4.00 m and moment of inertia 500 kg·m². A 60.0 kg student walks from the rim to the center.

• Tasks:

  • (a) Find the new angular speed when at the center.

  • (b) Work done by the student during walk.

Problem 11: Work Done Calculation

• Formula: W = KEf - KEi = - 1/I * IpWF * 1/2 X = 13323 1 4563 = 8760 J = -8.76 kJ.