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A ball bearing is dropped on to a rigid-hard surface from a height h. It rebounds to a height h1. Calculate the coefficient of restitution if h = 800 mm and h1 = 650 mm.

Physics

ScanSolve AI Answer

Answer

0.901\text{0.901}

Step-by-step solution

5 steps

Here's the solution for question 1.

  1. Identify the given values.

    The initial height is h=800 mmh = 800 \text{ mm}.
    The rebound height is h1=650 mmh_1 = 650 \text{ mm}.

  2. State the formula for the coefficient of restitution.

    The coefficient of restitution, ee, for a ball bouncing off a surface is given by the ratio of the square root of the rebound height to the square root of the initial height:

    e=h1he = \sqrt{\frac{h_1}{h}}
  3. Substitute the given values into the formula.

    e=650 mm800 mme = \sqrt{\frac{650 \text{ mm}}{800 \text{ mm}}}
  4. Calculate the coefficient of restitution.

    e=650800e = \sqrt{\frac{650}{800}} e=0.8125e = \sqrt{0.8125} e≈0.9013878e \approx 0.9013878
  5. Round the answer to an appropriate number of significant figures.

    e≈0.901e \approx 0.901

    The coefficient of restitution is unitless.

    The coefficient of restitution is 0.901\text{0.901}.

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