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Answer the physics question 3 and 4

Physics

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Answer

4 m/s\text{4 m/s}

0.08 J\text{0.08 J}

Step-by-step solution

5 steps
  1. Convert given values to SI units for Question 3.

    Mass m=20g=20×10−3kg=0.02kgm = 20 \text{g} = 20 \times 10^{-3} \text{kg} = 0.02 \text{kg}
    Extension x=4cm=4×10−2m=0.04mx = 4 \text{cm} = 4 \times 10^{-2} \text{m} = 0.04 \text{m}
    Force constant k=200Nm−1k = 200 \text{Nm}^{-1}

  2. Apply the principle of conservation of energy for Question 3.

    The elastic potential energy stored in the rubber is converted into the kinetic energy of the stone.

    Ep=EkE_p = E_k 12kx2=12mv2\frac{1}{2}kx^2 = \frac{1}{2}mv^2
  3. Substitute the values and solve for velocity vv for Question 3.

    12(200 Nm−1)(0.04 m)2=12(0.02 kg)v2\frac{1}{2}(200 \text{ Nm}^{-1})(0.04 \text{ m})^2 = \frac{1}{2}(0.02 \text{ kg})v^2 (200)(0.0016)=(0.02)v2(200)(0.0016) = (0.02)v^2 0.32=0.02v20.32 = 0.02v^2 v2=0.320.02v^2 = \frac{0.32}{0.02} v2=16v^2 = 16 v=16v = \sqrt{16} v=4 m/sv = 4 \text{ m/s}

    The velocity with which the stone leaves the catapult is 4 m/s\boxed{\text{4 m/s}}.

  4. Identify given values for Question 4.

    Compression x=0.02mx = 0.02 \text{m}
    Force constant k=400Nm−1k = 400 \text{Nm}^{-1}

  5. Calculate the energy stored in the spring for Question 4.

    The energy stored in a spring is given by the elastic potential energy formula:

    Ep=12kx2E_p = \frac{1}{2}kx^2 Ep=12(400 Nm−1)(0.02 m)2E_p = \frac{1}{2}(400 \text{ Nm}^{-1})(0.02 \text{ m})^2 Ep=12(400)(0.0004)E_p = \frac{1}{2}(400)(0.0004) Ep=200(0.0004)E_p = 200(0.0004) Ep=0.08 JE_p = 0.08 \text{ J}

    The energy stored in the spring is 0.08 J\boxed{\text{0.08 J}}.

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