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27 March, 20:05

What is the speed of the silver sphere at the moment it hits the ground? (Assume that energy is conserved during the fall and that 100% of the sphere's initial potential energy is converted to kinetic energy by the time impact occurs.)

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  1. 27 March, 21:11
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    Complete question:

    Consider the two spheres shown here, one made of silver and the other of aluminum. The spheres are dropped from a height of 2.1 m. (composition of sphere : density is 10.49 g/cm³, volume is 196 cm³), (composition of aluminum : density is 2.7 g/cm³, volume is 196 cm³).

    What is the speed of the silver sphere at the moment it hits the ground? (Assume that energy is conserved during the fall and that 100% of the sphere's initial potential energy is converted to kinetic energy by the time impact occurs.)

    Answer:

    The speed of the silver sphere at the moment it hits the ground is 6.416 m/s

    Explanation:

    Potential energy of the silver sphere = mgh

    where;

    g is acceleration due to gravity = 9.8 m/s²

    h is height above the ground = 2.1m

    m is mass of the silver sphere = ?

    Density = mass/volume

    mass of the silver sphere = density X volume = (10.49 g/cm³) X (196cm³)

    mass of the silver sphere = 2056.04 g = 2.056 kg

    Potential energy of the silver sphere = (2.056 X 9.8 X 2.1) J

    Potential energy of the silver sphere = 42.31248 J

    If energy is conserved and 100% potential energy is converted to kinetic energy, the speed of the silver sphere will be calculated as follows:

    Kinetic Energy (K. E) = 1/2mv²

    where;

    m is mass of the sphere in kg = 2.056kg

    v is the velocity of the silver sphere = ?

    If energy is conserved; Potential energy = Kinetic energy

    42.31248 = 1/2mv²

    v² = (42.31248 X 2) / m

    v² = (42.31248 X 2) / 2.056

    v² = 41.16

    v = √41.16

    v = 6.416 m/s

    Therefore, the speed of the silver sphere at the moment it hits the ground is 6.416 m/s
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