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A jar with mass of 10kg is measured in 1500g. Fluid. What is the density?
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Exercise
- A jar with mass of is measured in . 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 is a typo and should be (or ) for the volume of the fluid.
Convert the volume to cubic meters.
$$ V = 1500 \text{ cm}^3 = 1500 \times (10^{-2} \text{ m})^3 = 1500 \times 10^{-6} \text{ m}^3 = 1.5 \times 10^{-3} \text{ m}^3 $$Use the formula for density, .
$$ \rho = \frac{10 \text{ kg}}{1.5 \times 10^{-3} \text{ m}^3} $$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 . Filled with a mass of , calculate the volume of the boat.
Identify the given values
density () and mass ().
Use the formula for volume, .
$$ V = \frac{13 \text{ kg}}{250 \text{ kg/m}^3} $$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 tricycle that accelerates at a rate of ?
Identify the given values
mass () and acceleration ().
Use Newton's Second Law of Motion, .
$$ F = 20 \text{ kg} \times 6 \text{ m/s}^2 $$Calculate the force.
$$ F = 120 \text{ N} $$ The force is $\boxed{\text{120 N}}$.4. A vehicle speeds at with a force of . 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 (). The speed of 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 force.
- A car travels with a speed of for . Calculate the displacement.
Identify the given values
speed () and time ().
Use the formula for displacement, assuming constant speed
.
Calculate the displacement.
$$ d = 65 \text{ m} $$ The displacement of the car is $\boxed{\text{65 m}}$.
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