Mr. Keye Physics

Balanced Forces

Work this set after 4.1 Identifying Forces, 4.2 Free-Body Diagrams, and 4.6 A Force at an Angle.

This page has the nine scenarios, the scale and string, the two blocks against a wall, the hanging mass on angled ropes, and the bar over a scale. Every object in these problems is in equilibrium, so the forces on it add to zero, and that lets you find the magnitudes of unknown forces. Name every force as Force of 1 on 2, and draw the diagrams large.

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  1. There are nine physical scenarios below. For each one, identify the Forces applied to the object named. Some scenarios give the mass of the objects. If the mass is given, you can calculate the magnitude of the Force of gravity on that object. The Force of gravity on an object is also called the object's Weight in physics. Therefore, weight is not the same quantity as mass.

    Every identified Force will ALWAYS have two objects interacting, namely the object applying the Force and the object the Force is applied to.

    For each identified Force, state it in the following manner: Force of object 1 on 2. If a string pulled on block A you would say Force of string on block A, and write it as FS on AF_{S \text{ on } A}. The word on helps you distinguish which object you are analyzing.

    In a few of the scenarios there is a force labeled only FF. Use FF as its variable, with no subscript. Every force is exerted by another object, but a force labeled only FF means the object exerting it is not important to know about in that problem.

    Then state the direction of each Force. You won't know the exact angles, but you can use words like above and below together with the xx or yy direction if forces are not solely horizontal or vertical.

    When you draw a Free Body Diagram, use a ruler and draw it large, on a dot that abstractly represents the object. It is critical that the Force vectors you draw are correctly sized relative to each other. An arrow twice as long as another indicates twice as much Force, so do not draw the length of a Force vector haphazardly. Small diagrams are difficult to read and cause confusion.

    Use g=10  m/s2g = 10\;\text{m/s}^2 throughout.

    (a)

    Identify all Forces applied to the block.

    Select all that apply.

    (b)

    Identify all Forces applied to the block.

    Select all that apply.

    (c)

    Identify all Forces applied to block B.

    Select all that apply.

    (d)

    Identify all Forces applied to the 5  kg5\;\text{kg} block that hangs from the string.

    Select all that apply.

    Calculate the magnitude of the Force of gravity on the hanging block.

    N
    (e)

    Identify all Forces applied to the block on the incline.

    Select all that apply.

    (f)

    Identify all Forces applied to block B, the middle block.

    Select all that apply.

    Determine the magnitude of FA on BF_{A \text{ on } B}, the force block A exerts on block B.

    N

    Determine the magnitude of the force the ground exerts on block A.

    N
    (g)

    Identify all Forces applied to the ball.

    Select all that apply.

    (h)

    Identify all Forces applied to block A, the upper block.

    Select all that apply.

    (i)

    Identify all Forces applied to block A.

    Select all that apply.

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  2. The figure shows the same 5  kg5\;\text{kg} block in three arrangements, with a string and a scale. The scale reads in Newtons.

    Draw a free body diagram for the block in arrangement (b).

    (a)

    Determine the tension in the string in arrangement (a), where the block hangs clear of the scale.

    N
    (b)

    In arrangement (b) the block rests on the scale and the string tension is 20  N20\;\text{N}. What does the scale read?

    N
    (c)

    In arrangement (c) there is no string. What does the scale read?

    N
    (d)

    The three readings are 0  N0\;\text{N}, 30  N30\;\text{N} and 50  N50\;\text{N} for the same block. Explain what a scale measures, and why its reading is not always the weight of the block.

    Answer this in your own words, on paper or out loud, then compare.

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  3. A 10  N10\;\text{N} force pushes on Block A. Identify all forces on each block and draw a free body diagram for each block, and include the magnitude of each force in Newtons. The length of a force vector matters, and represents the magnitude of the force.

    (a)

    What is the magnitude of the force block B exerts on block A?

    N
    (b)

    What is the magnitude of the force the wall exerts on block B?

    N
    (c)

    What is the magnitude of the force the floor exerts on block B?

    N
    (d)

    Draw both free body diagrams, to scale, and label every arrow with its magnitude in Newtons. Then say which arrows must be drawn the same length as each other, and why.

    Answer this in your own words, on paper or out loud, then compare.

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  4. A 7  kg7\;\text{kg} mass hangs from rope C, which meets ropes A and B at point PP. The ropes are massless.

    Work through the parts in order. Point PP is analyzed as an object, in the same way as the hanging mass.

    (a)

    Identify all forces on the hanging mass.

    Select all that apply.

    (b)

    Determine the magnitude of the tension in rope C.

    N
    (c)

    Identify all forces on point PP.

    Select all that apply.

    (d)

    Determine the magnitude of the tension in rope A.

    N
    (e)

    Determine the magnitude of the tension in rope B.

    N
    (f)

    Draw the free body diagram for point PP, then show that ∑F⃗on point P=0\sum \vec{F}_{\text{on point }P} = 0 using your three tensions. Then explain, in words, why rope B carries more tension than rope A.

    Answer this in your own words, on paper or out loud, then compare.

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    • Newton's First Law

      Equilibrium is the first law's case: zero net force, so the velocity doesn't change.

      Review: Lesson 4.1: Identifying Forces

    • Trigonometry

      The components are the two short sides of a right triangle whose long side is the vector.

  5. A person pulls with 400  N400\;\text{N} on a rope that is hung around a pulley and attached to a 10  kg10\;\text{kg} bar. Another person whose mass is 50  kg50\;\text{kg} has his hands contacting the bar and is standing on a scale that reads in Newtons.

    Draw a free body diagram for the person on the scale.

    (a)

    Is the bar pushing down on the person, or pulling up on him?

    (b)

    Determine the reading on the scale.

    N
    (c)

    Now predict what the scale would read if the bar essentially had no mass.

    N
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