The unit Newton is equivalent to _?
A. kgm/s2
B. kg/m/s2
C. kg/ m2
D. kgms2
ii) A speed boat requires 80 kW to move at a constant speed of 15 m/s. What is the resistive force of the water at this speed?
The Correct Answer and Explanation is :
i) The unit Newton is equivalent to:
The correct answer is:
A. kg·m/s²
Explanation:
The Newton (N) is the SI unit of force. According to Newton’s second law of motion, force is the product of mass and acceleration. Mathematically, this can be expressed as:
[ F = m \times a ]
Where:
- F is the force (in Newtons),
- m is the mass (in kilograms, kg),
- a is the acceleration (in meters per second squared, m/s²).
Since acceleration has the units of meters per second squared (m/s²), and mass has the unit of kilograms (kg), the unit of force (Newton) can be derived as:
[
\text{Newton (N)} = \text{kg} \times \text{m/s}^2
]
This confirms that the unit of Newton is equivalent to kg·m/s².
ii) A speed boat requires 80 kW to move at a constant speed of 15 m/s. What is the resistive force of the water at this speed?
The correct answer can be found by using the formula for power:
[
\text{Power (P)} = \text{Force (F)} \times \text{Velocity (v)}
]
Where:
- Power (P) is 80 kW (kilowatts) = ( 80,000 \, \text{W} ),
- Velocity (v) is 15 m/s,
- Force (F) is the resistive force we need to find.
Rearranging the formula to solve for the force:
[
F = \frac{P}{v}
]
Substituting the given values:
[
F = \frac{80,000}{15} \, \text{N}
]
[
F \approx 5333.33 \, \text{N}
]
Thus, the resistive force of the water at this speed is approximately 5333.33 N.
Explanation:
In this scenario, the boat is moving at a constant speed of 15 m/s, which means that the net force acting on the boat is zero, implying that the resistive force (due to water resistance) is equal and opposite to the force provided by the boat’s engine. The power provided by the engine is converted into work to overcome the resistive force. The relationship between power, force, and velocity helps us determine the magnitude of this resistive force.
Let’s now generate a visual representation for this.
Here is an illustration showing the speed boat moving at a constant speed in the water, with the resistive force applied by the water. Let me know if you need any further details!
