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A jar with mass of 10kg is measured in 1500g. Fluid. What is the density?

Physics

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Exercise

  1. A jar with mass of 10 kg10 \text{ kg} is measured in 1500 J1500 \text{ J}. What is the density?
    • Assumption: The unit "J" (Joules) is a unit of energy, not volume. Given the context of density, it is assumed that 1500 J1500 \text{ J} is a typo and should be 1500 cm31500 \text{ cm}^3 (or 1500 mL1500 \text{ mL}) for the volume of the fluid.
  1. Convert the volume to cubic meters.

    $$
    V = 1500 \text{ cm}^3 = 1500 \times (10^{-2} \text{ m})^3 = 1500 \times 10^{-6} \text{ m}^3 = 1.5 \times 10^{-3} \text{ m}^3
    $$
    
  2. Use the formula for density, ρ=mV\rho = \frac{m}{V}.

    $$
    \rho = \frac{10 \text{ kg}}{1.5 \times 10^{-3} \text{ m}^3}
    $$
    
  3. Calculate the density.

    $$
    \rho = 6666.67 \text{ kg/m}^3
    $$
    The density of the fluid is $\boxed{\text{6666.67 kg/m}^3\text{}}$.
    

    2. The density of a boat is 250 kg/m3250 \text{ kg/m}^3. Filled with a mass of 13 kg13 \text{ kg}, calculate the volume of the boat.

  4. Identify the given values

    density (ρ\rho) and mass (mm). ρ=250 kg/m3 \rho = 250 \text{ kg/m}^3 m=13 kg m = 13 \text{ kg}

  5. Use the formula for volume, V=mρV = \frac{m}{\rho}.

    $$
    V = \frac{13 \text{ kg}}{250 \text{ kg/m}^3}
    $$
    
  6. Calculate the volume.

    $$
    V = 0.052 \text{ m}^3
    $$
    The volume of the boat is $\boxed{\text{0.052 m}^3\text{}}$.
    

    3. What is the force of a 20 kg20 \text{ kg} tricycle that accelerates at a rate of 6 m/s26 \text{ m/s}^2?

  7. Identify the given values

    mass (mm) and acceleration (aa). m=20 kg m = 20 \text{ kg} a=6 m/s2 a = 6 \text{ m/s}^2

  8. Use Newton's Second Law of Motion, F=maF = ma.

    $$
    F = 20 \text{ kg} \times 6 \text{ m/s}^2
    $$
    
  9. Calculate the force.

    $$
    F = 120 \text{ N}
    $$
    The force is $\boxed{\text{120 N}}$.
    

    4. A vehicle speeds at 10 m/s10 \text{ m/s} with a force of 500 N500 \text{ N}. Calculate the mass of the vehicle. * This problem cannot be solved as stated. To calculate the mass of the vehicle using the given force, the acceleration of the vehicle is required (F=maF=ma). The speed of 10 m/s10 \text{ m/s} alone is not sufficient to determine acceleration without additional information such as initial speed, time, or distance over which the force acts. If the speed is constant, the net force is zero, which contradicts the given 500 N500 \text{ N} force.

    1. A car travels with a speed of 13 m/s13 \text{ m/s} for 5 seconds5 \text{ seconds}. Calculate the displacement.
  10. Identify the given values

    speed (vv) and time (tt). v=13 m/s v = 13 \text{ m/s} t=5 s t = 5 \text{ s}

  11. Use the formula for displacement, assuming constant speed

    d=v×td = v \times t. d=13 m/s×5 s d = 13 \text{ m/s} \times 5 \text{ s}

  12. Calculate the displacement.

    $$
    d = 65 \text{ m}
    $$
    The displacement of the car is $\boxed{\text{65 m}}$.
    
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