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23 July, 21:22

A passenger in a train accelerating smoothly away from a station observes that a child's yo-yo hanging by its string from a luggage rack makes a 10 degree angle from the vertical. Calculate the train's acceleration?

Calculate the radius of a solid iron sphere that will have a terminal velocity of 100 m/s when dropped from a large height.

Density of iron is 7874 kg/m3. A sphere has Cd =.47. Use p = 1.3kgm3 for air

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  1. 23 July, 23:58
    0
    1.73 m/s²

    3.0 cm

    Explanation:

    Draw a free body diagram of the yo-yo. There are two forces: weight force mg pulling down, and tension force T pulling up 10° from the vertical.

    Sum of forces in the y direction:

    ∑F = ma

    T cos 10° - mg = 0

    T cos 10° = mg

    T = mg / cos 10°

    Sum of forces in the x direction:

    ∑F = ma

    T sin 10° = ma

    mg tan 10° = ma

    g tan 10° = a

    a = 1.73 m/s²

    Draw a free body diagram of the sphere. There are two forces: weight force mg pulling down, and air resistance D pushing up. At terminal velocity, the acceleration is 0.

    Sum of forces in the y direction:

    ∑F = ma

    D - mg = 0

    D = mg

    ½ ρₐ v² C A = ρᵢ V g

    ½ ρₐ v² C (πr²) = ρᵢ (4/3 πr³) g

    3 ρₐ v² C = 8 ρᵢ r g

    r = 3 ρₐ v² C / (8 ρᵢ g)

    r = 3 (1.3 kg/m³) (100 m/s) ² (0.47) / (8 (7874 kg/m³) (9.8 m/s²))

    r = 0.030 m

    r = 3.0 cm
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