Question
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A force of 5.0 N is applied to a \( 20-\mathrm{kg} \) mass on a horizontal frictionless surface. As the speed of the mass increases at a constant acceleration, the power delivered to it by the force: 1) remains the same. 2) increases. 3) decreases. 4) doubles every 4.0 seconds. 5) halves every 4.0 seconds.

Ask by Schultz Guerrero. in the United States
Feb 25,2025

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Answer

The power increases over time.

Solution

The work done by a force is converted into kinetic energy. When a force F is applied to an object moving at speed v, the instantaneous power delivered by the force is given by:   Power = Force × Velocity Since the acceleration is constant, the velocity increases linearly with time. As a result, even though the force is constant, the power (which is the product of force and velocity) increases over time. Thus, the answer is: 2) increases.

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The Deep Dive

As the \( 20-\mathrm{kg} \) mass accelerates under the constant force of \( 5.0 \, \text{N} \), the power delivered by the force increases. Power, defined as the rate at which work is done (or energy is transferred), is given by the formula \( P = F \cdot v \), where \( v \) is the velocity of the mass. As the mass accelerates, its velocity increases, and since the force remains constant, the power must increase as well. So, the correct answer is that the power delivered to the mass increases. Keep in mind that as you push an object to higher speeds, the power needed to keep it accelerating becomes more significant, like trying to keep up with a sprinting cheetah—it just gets faster and faster!

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