Question

Assess System 1 has a force of $10\mathrm{N}$ and a speed of $5\mathrm{m}/\mathrm{s}$. System 2 has a force of $20\mathrm{N}$ and a speed of $2\mathrm{m}/\mathrm{s}$. Which system has the greater power? Explain.

Short answer

System 1 has greater power at 50 W, compared to System 2's 40 W.

Step-by-step solution

Understanding the Formula for Power

Power is defined as the rate at which work is done. It can be calculated using the formula: $P=F\times v$, where $P$ is power, $F$ is force, and $v$ is speed.

Calculate Power for System 1

For System 1, the force $F=10\text{ N}$ and speed $v=5\text{ m/s}$. Using the power formula, $P_1=10\times 5=50\text{ W}$ (watts).

Calculate Power for System 2

For System 2, the force $F=20\text{ N}$ and speed $v=2\text{ m/s}$. Using the power formula, $P_2=20\times 2=40\text{ W}$ (watts).

Compare the Powers of Both Systems

System 1 has a power of 50 W, and System 2 has a power of 40 W. Therefore, System 1 has greater power than System 2.

Key concepts

Understanding Force: Push or Pull

In the context of physics, force is an interaction that causes an object to change its velocity or to move if it was initially at rest. It's essentially a push or a pull on an object. The unit of force in the International System of Units (SI) is the Newton, denoted by the symbol $\text{N}$. One Newton is defined as the amount of force needed to accelerate a one-kilogram mass by one meter per second squared in the direction of the applied force. When talking about power, force becomes an essential component because it helps determine how much work is done over a certain time period. To tie this back to our exercise, System 1 and System 2 were subjected to forces of 10 N and 20 N, respectively. Despite the stronger force in System 2, it was System 1 that ultimately had greater power, a reminder that force alone does not dictate power.

Speed: How Fast is it Going?

Speed refers to how fast something moves through a particular distance over a certain amount of time. It is a scalar quantity, which means it only has magnitude and no directional component. Commonly measured in meters per second ($\text{m/s}$), speed in our earlier exercise was crucial in calculating power for both systems.Understanding speed is imperative when discussing power. If you have a higher speed, it generally indicates that more work is done in less time. This factor is particularly compelling in the given systems where System 1 moves at 5 m/s while System 2 moves at 2 m/s, despite the higher force in System 2. So, even though System 2 had greater force, System 1 had a biological advantage through speed which led to increased power.

Work: Energy in Motion

Work in physics describes the amount of energy transferred by a force over a distance. The equation for work is $W=F\times d$, where $W$ is the work done, $F$ is the force applied, and $d$ is the distance over which the force is applied. Work is measured in Joules ($\text{J}$).Work's relationship to power—calculated as the rate at which work is done—ultimately clarifies how force and speed combine to impact power output. However, in the case of the two systems in our exercise, distance wasn’t considered. Instead, power was directly calculated using force and speed, demonstrating how work-energy principles are a foundational consideration in power equations. Work and power are interrelated because when more work is done faster, more power is displayed. Therefore, System 1, with a greater speed for its force, performed more work per unit time leading to higher power.