Problem 7 - Applied Physics

Question

An electric golf cart develops \(1.25 \mathrm{~kW}\) of power while moving at a constant speed. (a) Express its power in horsepower. (b) If the cart travels \(20 \overline{0} \mathrm{~m}\) in \(35.0 \mathrm{~s}\), what force is exerted by the cart?

Step-by-Step Solution

Answer

(a) 1.68 hp; (b) 218.6 N force exerted.

Step 1: Convert Power to Horsepower

To convert the given power from kilowatts to horsepower, we use the conversion factor: \[ 1 ext{ kW} = 1.34102 ext{ horsepower} \]The cart develops \(1.25\) kW of power. Let's perform the conversion:\[1.25 ext{ kW} \times 1.34102 ext{ hp/kW} = 1.676275 ext{ hp} \]Rounded, the power in horsepower is approximately \(1.68\) hp.

Step 2: Determine Speed

First, find the speed of the golf cart using the distance and time given. The formula for speed is:\[\text{Speed} = \frac{\text{Distance}}{\text{Time}} \]Plugging in the given values:\[\text{Speed} = \frac{200.0 \, \text{m}}{35.0 \, \text{s}} = 5.714 \, \text{m/s} \]

Step 3: Relate Power, Force, and Speed

Power is also related to force and speed. The formula is:\[\text{Power} = \text{Force} \times \text{Speed} \]We can rearrange this formula to solve for force:\[\text{Force} = \frac{\text{Power}}{\text{Speed}} \]

Step 4: Calculate Force

Substitute the known values of power (in watts) and speed into the equation to find the force. Note, 1 kW = 1000 W, so\[1.25 \, \text{kW} = 1250 \, \text{W} \]Thus, the force exerted is:\[\text{Force} = \frac{1250 \, \text{W}}{5.714 \, \text{m/s}} \approx 218.61 \, \text{N} \]Rounded, the force exerted by the cart is approximately \(218.6\, \text{N}\).

Key Concepts

Power Conversion

Understanding power conversion is crucial when dealing with different units. In physics, power is often measured in watts (W) or kilowatts (kW). However, horsepower (hp) is also a common unit, especially for vehicles.
To convert kilowatts to horsepower, we use the conversion factor:

• \(1\, \text{kW} = 1.34102\, \text{hp}\)

Using this, you can easily convert the power of any device like our electric golf cart from kilowatts to horsepower. In the example provided, the cart develops 1.25 kW. When converted:

• \(1.25\, \text{kW} \times 1.34102\, \text{hp/kW} = 1.676275\, \text{hp}\)

Rounded, this gives approximately 1.68 horsepower.
Remember, these conversions are helpful to understand the power capabilities of machinery in different contexts and preferred measurement systems.

Force Calculation

Force calculation can often seem complex, but breaking it down using the right formulas makes it simpler. In physics, the force exerted by an object moving at a constant speed can be determined using the power and speed.
The formula linking power, force, and speed is:

• \(\text{Power} = \text{Force} \times \text{Speed}\)

Rearranging gives us:

• \(\text{Force} = \frac{\text{Power}}{\text{Speed}}\)

In our exercise, we already calculated the power in watts (1.25 kW = 1250 W). With a known speed of 5.714 m/s, we substitute these values to find:

• \(\text{Force} = \frac{1250\, \text{W}}{5.714\, \text{m/s}} = 218.61\, \text{N}\)

Thus, the force exerted by the electric golf cart is approximately 218.6 N.
Understanding this calculation helps you determine what force is necessary to maintain a specific speed under certain power conditions.

Speed Determination

Speed is an essential concept in physics and everyday life. It tells us how fast an object is moving, and is calculated by dividing the distance traveled by the time taken.
To find speed, use the formula:

• \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\)

In the case of our golf cart, covering 200.0 meters in 35.0 seconds:

• \(\text{Speed} = \frac{200.0\, \text{m}}{35.0\, \text{s}} = 5.714\, \text{m/s}\)

This gives the average speed of the cart.
Understanding this basic calculation is crucial in physics as it lays the foundation for more complex problems involving motion and mechanics.

Physics Formulas

Physics relies heavily on a wide range of formulas to solve various problems. These formulas provide a framework to calculate and understand different physical aspects like motion, energy, and force. Knowing when and how to apply these formulas is crucial.
In our problem, we utilized:

• Power conversion (kW to hp): Uses a simple multiplication by the conversion factor 1.34102.
• Speed determination: Divides distance by time, paving the way to understanding movement.
• Power, force, and speed relationship: Relates how much power is needed to sustain constant speed through force.

By mastering these, you can tackle a wide variety of physics problems with confidence.
Each formula often builds upon concepts from others, providing a cohesive toolset to describe the physical world.