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densk [106]
3 years ago
10

The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of 2615

N with an effective perpendicular lever arm of 2.85 cm , producing an angular acceleration of the forearm of 110.0 rad / s2 . What is the moment of inertia of the boxer's forearm?
Physics
1 answer:
mart [117]3 years ago
7 0

Answer:

0.68 kg-m²

Explanation:

F = Force applied by the muscle = 2615 N

r = effective perpendicular lever arm = 2.85 cm = 0.0285 m

α = Angular acceleration of the forearm = 110.0 rad/s²

I  = moment of inertia of the boxer's forearm = ?

Torque is given as

τ = I α                                   eq-1

Torque is also given as

τ = r F                                   eq-2

using eq-1 and eq-2

r F =  I α

(0.0285)(2615) = (110.0) I

I = 0.68 kg-m²

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Answer:

a)  Δx = 49.23 mi , b)  Δx = 5.77 mi

Explanation:

As we have an acceleration function we must use the definition of kinematics

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we integrate and evaluators

      v - vo = ∫ (-1280 (1 + 8t)⁻³ dt = -1280 ∫ (1+ 8t)⁻³ dt

We change variables

       1+ 8t = u

       8 dt = du

       v - v₀ = -1280 ∫ u⁻³ du / 8

       v -v₀ = -1280 / 8 (-u⁻²/2)

       v - v₀ = 80 (1+ 8t)⁻²

We evaluate between the initial t = 0 v₀ = 80 and the final instant t and v

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      v = 80 (1+ 8t)⁻²

We repeat the process for defining speed is

     v = dx / dt

    dx = vdt

    x-x₀ = 80 ∫ (1-8t)⁻² dt

    x-x₀ = 80 ∫ u⁻² dt / 8

    x-x₀ = 80 (-1 / u)

    x-x₀ = -80 (1 / (1 + 8t))

We evaluate for t = 0 and x₀ and the upper point t and x

   x -x₀ = -80 [1 / (1 + 8t) - 1]

We already have the function of time displacement

a) let's calculate the position at the two points and be

t = 0 h

     x = x₀

t = 0.2 h

    x-x₀ = -80 [1 / (1 +8 02) -1]

    x-x₀ = 49.23

displacement is

  Δx = x (0.2) - x (0)

   Δx = 49.23 mi

b) in the interval t = 0.2 h at t = 0.4 h

t = 0.4h

     x- x₀ = -80 [1 / (1+ 8 0.4) -1]

     x-x₀ = 55 mi

    Δx = x (0.4) - x (0.2)

     Δx = 55 - 49.23

     Δx = 5.77 mi

3 0
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