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19 January, 21:12

Four weightlifters (A-D) enter a competition. The mass, distance, and time of their lifts are shown in the table.

Weightlifter Mass (kg) Distance (m) Time (s)

A 100.0 2.25 0.151

B 150.0 1.76 0.052

C 200.0 1.50 0.217

D 250.0 1.25 0.206

Which weightlifter has the least power?

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  1. 19 January, 21:47
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    Let Pa, Pb, Pc, and Pd be the powers delivered by weightlifters A, B, C, and D, respectively.

    Use this equation to determine each power value:

    P = W:Δt

    P is the power, W is the work done by the weightlifter, and Δt is the elapsed time.

    A) Determining Pa:

    Pa = W:Δt

    The weightlifter does work to lift the weight up a certain distance. Therefore the work done is equal to the weight's gain in gravitational potential energy. The equation for gravitational PE is

    PE = mgh

    PE is the potential energy, m is the mass of the weight, g is the acceleration of objects due to earth's gravity, and h is the distance the weight was lifted.

    We can equate W = PE = mgh, therefore we can make the following substitution:

    Pa = mgh:Δt

    Given values:

    m = 100.0kg

    g = 9.81m/s²

    h = 2.25m

    Δt = 0.151s

    Plug in the values and solve for Pa

    Pa = 100.0*9.81*2.25:0.151

    Pa = 14600W (watt is the SI derived unit of power)

    B) Determining Pb:

    Let us use our new equation derived in part A to solve for Pb:

    Pb = mgh:Δt

    Given values:

    m = 150.0kg

    g = 9.81m/s²

    h = 1.76m

    Δt = 0.052s

    Plug in the values and solve for Pb

    Pb = 150.0*9.81*1.76:0.052

    Pb = 49800W

    C) Determining Pc:

    Pc = mgh:Δt

    Given values:

    m = 200.0kg

    g = 9.81m/s²

    h = 1.50m

    Δt = 0.217s

    Plug in the values and solve for Pc

    Pc = 200.0*9.81*1.50:0.217

    Pc = 13600W

    D) Determining Pd:

    Pd = mgh:Δt

    Given values:

    m = 250.0kg

    g = 9.81m/s²

    h = 1.25m

    Δt = 0.206s

    Plug in the values and solve for Pd

    Pd = 250.0*9.81*1.25:0.206

    Pd = 14900W

    Compare the following power values:

    Pa = 14600W, Pb = 49800W, Pc = 13600W, Pd = 14900W

    Pc is the lowest value.

    Therefore, weightlifter C delivers the least power.
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