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2.6: Chapter 2 Homework Problems

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    Exercise \(\PageIndex{1}\)

    A 30 kg barrel is sitting on a handcart as shown below. Determine the normal forces at A and B.

    A 30-kg barrel sits on a handcart, which is tilted backwards so the cart's upright arm is 60 degrees above the horizontal and the cart's base is 30 degrees above the horizontal. A is the point of contact between the barrel and the cart's upright arm; B is the point of contact between the barrel and the cart's base.
    Figure \(\PageIndex{1}\): problem diagram for Exercise \(\PageIndex{1}\); a barrel sitting in a tilted handcart.
    Answer

    \(F_A = 147.15 \, N; \, F_B = 254.87 \, N\).

    Exercise \(\PageIndex{2}\)

    A 0.25kg ball rolls into a corner as shown below. Assuming the surfaces are smooth (no friction), determine the normal forces at A and B.

    A ball is wedged in a crack: the left side of the crack is 20 degrees to the right of vertical, and the right side is 20 degrees above the horizontal.
    Figure \(\PageIndex{2}\): problem diagram for Exercise \(\PageIndex{2}\); a ball wedged into a narrow corner.
    Answer

    \(F_A = 1.09 \, N; \, F_B = 3.01 \, N\)

    Exercise \(\PageIndex{3}\)

    A traffic light is supported by two cables as shown below. The tension in cable one is measured to be 294.8 N. What is the tension in cable two? What is the mass of the traffic light?

    A traffic light is held in midair by two cables. The cable on the left is 15 degrees above the horizontal, and the cable on the right is 25 degrees above the horizontal.
    Figure \(\PageIndex{3}\): problem diagram for Exercise \(\PageIndex{3}\); a traffic light suspended by two angled cables.
    Answer

    \(T_2 = 276.6 \, N; \, m = 20 \, kg\)

    Exercise \(\PageIndex{4}\)

    A 50 kg truck engine is lifted using the setup shown below. Assuming that the pulleys shown in the diagram are frictionless, what force \(P\) must be applied to the cable to hold the engine in the position shown below with \(d\) = 1 meter? (Hint: Draw a free body diagram of the pulley supporting the engine block)

    An engine block is held in midair by a cable, which has its left end attached to the ceiling and its right end running through a pulley attached to the ceiling, 3 meters apart. There is a distance of d between the engine block and ceiling, and a force of P pulling down on the cable's free end.
    Figure \(\PageIndex{4}\): problem diagram for Exercise \(\PageIndex{4}\); an engine block suspended by a cable running through one anchor point and one pulley.
    Answer

    \(P = 442.1 \, N\)

    Exercise \(\PageIndex{5}\)

    Two weights are supported via cables as shown below. If body B has a weight of 60 pounds, what is the expected weight of body A based on the angles of the cables?

    Blocks A and B hang from a single cable stretched between two vertical walls. The cable segment connecting A to the left wall is at 32 degrees above the horizontal, the segment connecting A and B is at 12 degrees above the horizontal with A being higher than B, and the segment connecting B to the right wall is at 38 degrees above the horizontal.
    Figure \(\PageIndex{5}\): problem diagram for Exercise \(\PageIndex{5}\); two weights hanging from a single cable with fixed ends.
    Answer

    \(F_{gA} = 24.89 \, lbs\)

    Exercise \(\PageIndex{6}\)

    Three equally sized cylinders, each with mass 100 kg, are stacked in a groove as shown below. Determine all forces acting on cylinder C and show them in a diagram.

    A straight-sided groove with the left side 30 degrees above the horizontal and the right side 45 degrees above the horizontal. Three cylinders are stacked on their sides in the groove, with C being the deepest in the groove, A being to the left of C, and B being to the right of C. A and B are each tangent to C.
    Figure \(\PageIndex{6}\): problem diagram for Exercise \(\PageIndex{6}\); three balls wedged in a groove with angled sides.
    Answer

    \(F_{AC} = 490.5 \, N; \, F_{BC} = 693.7 \, N; \, F_{C1} = 1304.6 \, N; \, F_{C2} = 829.7 \, N; \, F_g = 981 \, N\)

    Exercise \(\PageIndex{7}\)

    You are hanging a pterodactyl model from the ceiling of a museum with three cables as shown below. Assuming the pterodactyl model has a mass of 260 kg, what is the tension we would expect in each of the three cables?

    A pterodactyl model hangs from 3 cables, drawn on a 3-dimensional coordinate plane. Cable A makes a 25-degree angle above the x-axis in the negative direction, cable B makes a 30-degree angle above the z-axis in the negative direction, and cable C makes a 20-degree above the xz plane with its projection onto said plane making a 30-degree angle below the positive x-axis.
    Figure \(\PageIndex{7}\): problem diagram for Exercise \(\PageIndex{7}\); a pterodactyl model hanging from the intersection of three unequally angled cables attached to the ceiling.
    Answer

    \(T_A = 2306.94 \, N; \, T_B = 1393.86 \, N; \, T_C = 2569.19 \, N\)

    Exercise \(\PageIndex{8}\)

    A hot air balloon is tethered as shown below. Assuming that the balloon is pulling upward with a force of 900 lbs, determine the tension in each of the cables.

    A hot air balloon tethered to the ground by 3 cables, drawn on a 3-dimensional coordinate plane. The balloon is 30 ft above the origin. Cable A meets the ground 30 ft to the left of the origin; B meets the ground 35 ft to the right of, and 20 ft in front of, the origin; C meets the ground 20 ft behind, and 10 ft to the right of, the origin.
    Figure \(\PageIndex{8}\): problem diagram for Exercise \(\PageIndex{8}\); a hot air balloon tethered to the ground by three unequally spaced cables.
    Answer

    \(T_A = 545.5 \, lbs; \, T_B = 430.7 \, lbs; \, T_C = 320.7 \, lbs\)

    This page titled 2.6: Chapter 2 Homework Problems is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jacob Moore & Contributors (Mechanics Map) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.