Select the correct answer.
A water pump with a power of $3.4 \times 10^2$ watts lifts water at the rate of $7.5 \times 10^{-2}$ meters/second from a water tank. What is the force exerted by the pump on the water?
A. $1.5 \times 10^3$ newtons
B. $2.2 \times 10^3$ newtons
C. $4.5 \times 10^3$ newtons
D. $5.4 \times 10^3$ newtons
Answer (2)
The problem requires finding the force exerted by a water pump using the given power and water lifting rate.
Recall the formula relating power, force, and velocity: P = F v .
Rearrange the formula to solve for force: F = v P , and substitute the given values: F = 7.5 × 1 0 − 2 3.4 × 1 0 2 .
Calculate the force: F ≈ 4.5 × 1 0 3 newtons, so the answer is 4.5 × 1 0 3 newtons .
Explanation
Understanding the Problem We are given the power of a water pump and the rate at which it lifts water. We need to find the force exerted by the pump on the water.
Recalling the Formula The relationship between power, force, and velocity is given by the formula: P = F v where:
P is the power (in watts)
F is the force (in newtons)
v is the velocity (in meters/second)
Identifying Given Values We are given:
P = 3.4 × 1 0 2 watts
v = 7.5 × 1 0 − 2 meters/second We need to find F .
Rearranging the Formula Rearrange the formula to solve for force: F = v P
Substituting Values Substitute the given values into the formula: F = 7.5 × 1 0 − 2 3.4 × 1 0 2 F = 0.075 340 F = 4533.333...
Calculating the Force The force exerted by the pump on the water is approximately 4533.33 newtons. We can express this in scientific notation as 4.53333 × 1 0 3 newtons. Comparing this to the given options, the closest answer is 4.5 × 1 0 3 newtons.
Final Answer The force exerted by the pump on the water is approximately 4.5 × 1 0 3 newtons. Therefore, the correct answer is C.
Examples
Understanding the relationship between power, force, and velocity is crucial in many real-world applications. For example, when designing a car engine, engineers need to calculate the force required to move the car at a certain speed, given the engine's power output. Similarly, in robotics, understanding this relationship helps in designing actuators that can exert the necessary force to perform specific tasks. This concept is also vital in understanding how machines like elevators and cranes function, where power is used to lift heavy objects against gravity.
The force exerted by the water pump is approximately 4.5 × 1 0 3 newtons, calculated using the formula F = v P . The correct answer from the provided options is C. 4.5 × 1 0 3 newtons.
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