The power of a motor pump is \(2 \mathrm{~kW}\). How much water per minute can the pump raise to a height of \(10 \mathrm{~m}\) ? (Under the influence of gravitational force, work = mass \((\mathrm{m}) \times\) gravitational field strength \((g) \times\) height \((h)\), where \(g=10 \mathrm{~ms}^{-2}\).) A. \(1,200 \mathrm{~kg}\) B. \(1,200 \mathrm{~g}\) C. \(120 \mathrm{~kg}\) D. \(120 \mathrm{~g}\)

The relationship between power and work is fundamental in physics. Power is defined as the rate at which work is done over time. In mathematical terms, it’s expressed as:
\ \( \text{Power} = \frac{\text{Work}}{\text{Time}} \).

This formula tells us that the amount of work done depends on the power output and the time over which the power is applied.
For instance, if a motor pump has a power rating of 2 kW (2000W) and operates for 60 seconds (one minute), we can determine the work performed:
\ \( \text{Work} = \text{Power} \times \text{Time} = 2000\text{ W} \times 60\text{ s} = 120,000 \text{ J} \).

This calculation shows how energy (in joules) is expended by the motor pump.

• **Key takeaways**
• Power tells us how quickly work is being done.
• Work is the result of energy transfer over time.

Put simply, the more powerful a pump, the more work it can do in a shorter amount of time.

Gravitational force is the attractive force that acts between any two masses. On Earth, this force gives weight to physical objects and causes them to fall towards the ground when dropped. The strength of the gravitational field at Earth's surface is approximately \( 9.8 \text{ m/s}^2 \), but for simplicity in many problems, it is rounded to \( 10 \text{ m/s}^2 \).

When calculating work related to lifting objects against gravitational force, we use the formula:

• \ \( \text{Work} = m \times g \times h \)

where:

• \( m \) is mass in kilograms
• \( g \) is gravitational field strength
• \( h \) is height in meters

For example, to raise water to a height of 10 meters, the work done against gravity will be directly proportional to the mass being lifted. If we know that \( 120,000 \text{ J} \) of work is needed to lift the water, we can set up the equation \( 120,000 = m \times 10 \times 10 \). Solving for \( m \) gives us that the mass of the water is 1200 kg.

This illustrates how gravitational force impacts the effort needed to elevate objects to a certain height.

In physics problems, mass and height often work together, especially when considering potential energy and work done against gravity. Mass (\( m \)) of an object is a measure of the amount of matter it contains and is typically measured in kilograms.

Height (\( h \)) refers to how high an object is raised above a reference point (usually the ground). When an object is elevated, it gains gravitational potential energy which is calculated as:

\ \( \text{Potential Energy} = m \times g \times h \).

This formula quantifies the energy based on the object's mass and height within a gravitational field. For the motor pump problem, raising water to 10 meters (height) means calculating how much mass can be lifted given a certain amount of work or energy. The relationship can simplify solving many physics problems involving lifting objects.

• **Key Points to Remember**
• The mass of an object affects how much potential energy it can have.
• The higher an object is lifted, the more work is required against gravity.
• Understanding these relationships can make solving for unknown variables easier in physics problems.

Remember, knowing the values of mass and height are essential when calculating work and energy, especially in scenarios involving lifting or moving objects within a gravitational field.