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What is impulse and what is its magnitude when a golf ball is hit?

Physics

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Answer

1.89 kg⋅m/s\text{1.89 kg}\cdot\text{m/s}

556.5 N\text{556.5 N}

Step-by-step solution

6 steps

3.1: Impulse is defined as the change in momentum of an object. It is also equal to the product of the net force acting on an object and the time interval over which the force acts.

3.2:

  1. Identify the given values and the formula for impulse.

    The mass of the golf ball is m=0.044 kgm = 0.044 \text{ kg}.
    The initial velocity is vi=0 m/sv_i = 0 \text{ m/s} (since it's initially at rest).
    The final velocity is vf=43 m/sv_f = 43 \text{ m/s}.
    The formula for impulse (JJ) is the change in momentum: J=Δp=mvf−mviJ = \Delta p = m v_f - m v_i.

  2. Substitute the values into the formula.

    J=(0.044 kg)(43 m/s)−(0.044 kg)(0 m/s)J = (0.044 \text{ kg})(43 \text{ m/s}) - (0.044 \text{ kg})(0 \text{ m/s})
  3. Calculate the magnitude of the impulse.

    J=1.892 kg⋅m/s−0 kg⋅m/sJ = 1.892 \text{ kg} \cdot \text{m/s} - 0 \text{ kg} \cdot \text{m/s} J=1.892 kg⋅m/sJ = 1.892 \text{ kg} \cdot \text{m/s}

    The direction of the impulse is in the direction the ball leaves the tee.
    The magnitude of the impulse is 1.89 kg⋅m/s\boxed{\text{1.89 kg}\cdot\text{m/s}}.
    The direction of the impulse is in the direction the ball leaves the tee.

    3.3:

  4. Identify the impulse and the contact time.

    From 3.2, the impulse J=1.892 kg⋅m/sJ = 1.892 \text{ kg} \cdot \text{m/s}.
    The contact time is Δt=3.4×10−3 s\Delta t = 3.4 \times 10^{-3} \text{ s}.
    The formula for average force (FavgF_{avg}) is Favg=JΔtF_{avg} = \frac{J}{\Delta t}.

  5. Substitute the values into the formula.

    Favg=1.892 kg⋅m/s3.4×10−3 sF_{avg} = \frac{1.892 \text{ kg} \cdot \text{m/s}}{3.4 \times 10^{-3} \text{ s}}
  6. Calculate the magnitude of the average force.

    Favg=556.4705... NF_{avg} = 556.4705... \text{ N} Favg≈556.5 NF_{avg} \approx 556.5 \text{ N}

    The magnitude of the average force is 556.5 N\boxed{\text{556.5 N}}.

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