## Selected Solutions To Problems & Exercises

1. 2 × 1010

7. 208 W 141 s

9. 3.20 s 4.04 s

11. 9.46 × 107 J 2.54 y

13. Identify knowns: m = 950 kg, slope angle * *= 2.00º, *v *= 3.00 m/s, *f *= 600 N

Identify unknowns: power *P* of the car, force *F* that car applies to road

Solve for unknown: P=\frac=\frac=F\left=Fv\\, where *F* is parallel to the incline and must oppose the resistive forces and the force of gravity: F=f+w=600\text+mg\sin\theta\\.

Insert this into the expression for power and solve:

\beginP& =& \leftv\\\text& =& \left\left\\\text& =& 2.77\times 10^4\text\end\\

About 28 kW is reasonable for a car to climb a gentle incline.

- College Physics. : OpenStax College.
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## What Is The Formula For Work Output

**The formula calculating work output is F*D/T, where F is the force exerted, D is the distance and T is the time.** The work output of a system is also described as its Power.

In order for work to be done, force has to be applied in the direction of the motion. Using this, work is calculated as Force * Distance. For example, if a man pushes an object with a force of 200N across a distance of 3M, the work done is 200 N * 3 M = 600 Nm or 600 J.

The work output or Power refers to the rate at which work is done. Power is measured in watts. Power is also sometimes measured in horsepower, where one horsepower is equal to 750 watts. Work output can be calculated using the formula Work done/time. For instance, if an electric motor raises a 1000kg beam, 4 meters in 10 seconds, where g is equal to 9.8,m/s, then the power is calculated as:

Work done/time = Force*distance/time = *4 /10 = 3920 watts. The higher the power of a machine, the more quickly it will be able to achieve a specific task. For instance, in the example above, a machine with a power rating of 8000 watts or higher would be able to lift the beam across the same distance in half the time.

## What Is A Watt

The concept of power was introduced by James Watt, the Scottish inventor who is better known for his work on steam engines. He conceived of power as the product of force *F* and velocity *v*, and that definition of power is still valid. In other words, if you keep applying a force *F* to a body while it is moving with a velocity *v*, the power expended is

Watt did all of his measurements using English units, and he invented the horsepower, which he defined as the power necessary to raise a load of 33,000 pounds one foot every minute.

When the metric system was adopted by the international scientific community, a watt, by virtue of it being a unit of work or energy over time, became equal to a joule per second. Since work *W* is force *F* times distance *d*, a joule is equal to a newton-meter, because newtons are the units of force. That makes 1 watt equal to 1 newton-meter / second.

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## Work Done By A Force Example Problems With Solutions

**Example 1: ** How much work is done by a force of 10N in moving an object through a distance of 1 m in the direction of the force ?**Solution: ** The work done is calculated by using the formula:W = F × SHere, Force F = 10 NAnd, Distance, S = 1 mSo, Work done, W = 10 × 1 J= 10 JThus, the work done is 10 joules

**Example 2: ** Find the work done by a force of 10 N in moving an object through a distance of 2 m.**Solution: ** Work done = Force × Distance movedHere, Force = 10 NWork done, W = 10 N × 2 m= 20 Joule = 20 J

**Example 3: ** Calculate the work done in pushing a cart, through a distance of 100 m against the force of friction equal to 120 N.**Solution: ** Force, F = 120 N Distance, s = 100 mUsing the formula, we haveW = Fs = 120 N × 100 m = 12,000 J

**Example 4: ** A body of mass 5 kg is displaced through a distance of 4m under an acceleration of 3 m/s2. Calculate the work done.**Sol.** Given: mass, m = 5 kgacceleration, a = 3 m/s2Force acting on the body is given byF = ma = 5 × 3 = 15 NNow, work done is given byW = Fs = 15 N × 4 m = 60 J

**Example 5: ** Calculate the work done in raising a bucket full of water and weighing 200 kg through a height of 5 m. .**Solution: ** Force of gravitymg = 200 × 9.8 = 1960.0 Nh = 5 mWork done, W = mghor W = 1960 × 5 = 9800 J

**Example 7: ** An engine does 64,000 J of work by exerting a force of 8,000 N. Calculate the displacement in the direction of force.**Solution: ** Given W = 64,000 J F = 8,000 NWork done is given by W = Fsor 64000 = 8000 × sor s = 8 m

## Work Efficiency Formula In Practice

Physicists and engineers use work efficiency when determining how productive and energy-conservative processes are for electrical circuits , thermal heat engines , radioactive process , other processes including quantum mechanics .

The simple ratio of output to input means scientists and engineers can used their simplified, universalized mathematical formulas for whatever type of efficiency or purpose they need. For example, you may use the ratio of power an antenna radiates to the power it absorbs at its terminals when detecting radio frequencies as a measure of efficiency.

Efficiency is more commonly expressed as a percentage as it directly compares the two factors, input and output. However, there are cases in which efficiency can be measured without a percentage such as **specific impulse**, the momentum divided by mass for a rocket by taking into account how it uses propellant or fuel as well as air resistance and other forces. Specific impulse gives physicists and engineers to determine thrust, efficiency and measures of propellant usage when designing an engine.

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## Mechanical Advantage Of Aluminum

You can also test simple machines like wedges or pulleys made of aluminum for their efficiency in using forces you apply to them. The more efficient these machines are in using the force applied to them, the higher their mechanical advantage is. These machines like pulleys or levers have an ideal mechanical advantage , or the ratio of the force they output to the force applied to them.

An ideal mechanical advantage formula is *F0/Fi* for the output force *Fo* to input force *Fi*. Different alloys of aluminum have different mechanical properties, leading to differences in mechanical advantage.

You can also mesaure the ideal mechanical advantage as *do/di _for the output distance _do* over which the force is exerted, and the input distance *di*. This would equal the distance you pull one rope of a pulley or the distance a lever travels when used as a simple machine.

This works because, according to conservation of energy, the work put into a system equals the work the system exerts. Work is the product of force and distance. If *Wi = Wo* for input work *Wi* and output work *Wo* and *IMA = F0/Fi*, then *Fo x do = Fi x di* and *IMA = do/di*.

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## How To Calculate Work Input In A Pulley

Every natural event has an equation to determine its outcome. When two objects come together to produce work, the energy generated by one object may need to be multiplied to affect the other. Pulley systems multiply force. Work creates force, and though force may be multiplied by the use of pulleys, the amount of work input remains the same. To calculate work input in a single pulley or a system of pulleys, you must learn the equations that determine the outcome of these laws of relativity, and how gravity, energy, and force affect our physical world.

Set up a single pulley system where the pulley is secured to the overhead support and the cord is run over the top. Create a loop at one end of the cord where the scale can be inserted into the opening and then pulled, once a mass is attached to the other end. Write down the law of work input and work output. In a pulley system without friction, work input equals work output: Work = Work .

Attach a known mass to the other end of the cord. It will be necessary to determine force when you want to calculate the work input in a pulley or a system of pulleys. Work is determined by multiplying force by distance traveled: Work = Force X Distance W=Fd. Write this equation down to use when you want to calculate work input in a pulley or a system of pulleys.

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## Watts As Units Of Electrical Power

The power formula for a circuit with a voltage *V* and current *I* is

You can use Ohm’s law to express either voltage or current in terms of the resistance *R* in the circuit: *V* = *I* × *R*. Doing so allows you to express power as a function of either voltage and current or voltage and resistance.

After making your measurements, you don’t have to do the calculations yourself. You can use an online calculator. There is one such calculator in Resources.

To get the result in watts, you must express voltage in volts, current in amperes and resistance on ohms. Thus, the watt can be expressed in these units:

1 watt = 1 volt-amp = 1 amp2-ohm = 1 volt2 / ohm.

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## Example 1 Calculating The Power To Climb Stairs

What is the power output for a 60.0-kg woman who runs up a 3.00 m high flight of stairs in 3.50 s, starting from rest but having a final speed of 2.00 m/s?

Figure 2. When this woman runs upstairs starting from rest, she converts the chemical energy originally from food into kinetic energy and gravitational potential energy. Her power output depends on how fast she does this.

#### Strategy and Concept

The work going into mechanical energy is *W*= KE + PE. At the bottom of the stairs, we take both KE and PEg as initially zero thus, W=\text_}+\text_}=\fracmv_}^2+mgh\\, where *h* is the vertical height of the stairs. Because all terms are given, we can calculate *W* and then divide it by time to get power.

#### Solution

Substituting the expression for *W* into the definition of power given in the previous equation, P=\frac\\ yields

\displaystyle=\frac=\fracmv_}^2+mgh}\\

Entering known values yields

\begin\\& =& \frac)^2+\left\left\left}}\\\text& =& \frac+1764\text}}\\\text& =& 538\text\end\\

#### Discussion

The woman does 1764 J of work to move up the stairs compared with only 120 J to increase her kinetic energy thus, most of her power output is required for climbing rather than accelerating.

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## How To Calculate Work Done

If you want to know how to find work by hand then follow these steps:

- Firstly, find force using its formula, which is F = ma.
- Measure the angle.
- Then convert values into SI units and plug in all the values in the formula for work and solve it.

Otherwise, you can determine work and related terms by plug in the known values in the work calculator.

**Example: Word with force and displacement.**

Find the work done by the force?

Force = 15 N

## Example Work Efficiency Calculation

A pulley rope that pulls a 10 pound weight 1 foot off the ground due to a human applying 6 pounds of force to pull the pulley rope 2 feet has these specific input and output forces. The human force, the input force, performs 6 pounds times 2 feet of work, or 12 foot-pounds of work. The machine’s motion, the output force, is then 10 pounds times 1 foot of work, or 10 foot-pounds of work.

The work efficiency is then the ratio of output to input in percentage form. This would be 10/12, or 0.83. Multiply this by 100 to convert to a percentage, which would give a work efficiency of 83 percent.

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## Coasting Down A Mountain Road

Consider the case of a vehicle that starts at rest and coasts down a mountain road, the workenergy principle helps compute the minimum distance that the vehicle travels to reach a velocity *V*, of say 60 mph . Rolling resistance and air drag will slow the vehicle down so the actual distance will be greater than if these forces are neglected.

Let the trajectory of the vehicle following the road be **X** which is a curve in three-dimensional space. The force acting on the vehicle that pushes it down the road is the constant force of gravity **F** = , while the force of the road on the vehicle is the constraint force **R**. Newton’s second law yields,

- F

- ft . }=8.3}},\quad }\quad s=8.3}}\approx 2000}.}

This formula uses the fact that the weight of the vehicle is *W* = *mg*.

## Why Is Work Done On The System Considered When Calculating The Work Output

The thermodynamic efficiency $\eta$ is calculated by $\eta= \frac}}$

Using the first law of thermodynamics we usually say that $W_$ is $Q_c+Q_h$, where $Q_c$ is the heat dissipated into a cold reservoir, and $Q_h$ is the heat absorbed by a hot reservoir. Both are measured within the system, such that $Q_c< 0$ and $Q_h> 0$

However I object to that. $W_$ is not $Q_c+Q_h$. That calculation is simply the magnitude of net energy in the process due to work. Namely, its considering the $W_$, done by the surroundings on the gas, to calculate the $W_$.

Consider the a Carnot engine. I would say that the work output is the area underneath the expansion isotherm, and the expansion adiabat. All other works are done on the system and are not “outputs”.

You might say that the other works are “negative outputs”. But although this makes sense in a mathematical sense, it doesn’t make practical sense that this should be a $W_$.

I’m obviously wrong about this, so I’d like someone to clear things up for me. Thanks.

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## Can Someone Do This Impossible Problem

If you lift a box 60 m with a force of 120 N what is the output work? If you push the same box 200 m up a ramp to the same height with the force of 25 N what is the input work? And what is the efficiency and mechanical advantage of the ramp?

This problem simply requires you to follow the definition of work.. Work is the energy transfer that occurs when an object is displaced over a distance h by an external force acting in the direction of displacement.

Work = Force x Displacement

= 120N * 60m

= 7200 J

Note this energy is stored as the potential energy of the object. It is also the amount of energy that will be released if the object was allowed to fall back to ground .

When you push the same block up a ramp instead of lifting it the work performed is

Work = 25N * 200m

= 5000 J

Mechanical Advantage of an inclined plane is = distance load is pushed/ height to which it gets raised.

= 200m/60m

= 3. 333

Efficiency of the ramp = 100* output energy/input energy .

Based on stated ‘output energy’ and ‘input energy’ in the problem statement this efficiency is > 100%, which is physically impossible. There is likely some piece of info missing from the problem or an inaccuracy. Sorry, this one does not make sense.

## How Do I Calculate Output Voltage From A Given Supply Voltage And Resistance

I have searched everywhere but I can’t seem to find out how I can calculate the output voltage from the resistance of a resistor and the supply voltage. Everything seemed to be about Ohm’s Law, which looks like it could help but I don’t know how.

In the case I need to solve, there is a supply of 5v and I need to get the resistance needed to lower the voltage for an LED to 3v. I will definitely need to do this operation again so if you could give something like an equation, rather than the necessary resistance.

LED’s are not like your standard circuit elements. Voltage current relation is highly nonlinear, so you don’t generally speak the LED having a unique resistance.

The voltage vs current relation is almost vertical at the operating voltage, i.e. you will have a huge range of currents with voltage very close to say 3V. The resistance of the LED can be almost anything, depending on current. Choosing the resistor to make the voltage across the LED is getting it backwards. The LED will adjust its own internal resistance to keep its voltage drop near 3V , the purpose of the external resistor is to limit the current through the LED so that it does not damage itself. You start with the current Imax you want to limit to, assume 3V accross the LED, solve 5V = 3V + R*Imax.

You need to know the resistance of the LED: call this $R_$ and call the resistor $R$. The current flowing out of the power supply is just the voltage divided by total resistance, $I = V/R$, so:

$$I = \frac }$$

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## How Do You Find The Work Output

**work output****work output****work****work**

. Beside this, what is the formula for work output?

The **formula** to calculate **work** efficiencyis the ratio of **output** to input expressed as a percentage.For a machine, you can determine the **work** put into themachine depending on how the machine works. You can generallycalculate **work** by multiplying the force times distance forthe motion.

Furthermore, what does work output mean? In physics, **work output is the work** done by asimple machine, compound machine, or any type of engine model. Incommon terms, it **is the** energy **output**, which forsimple machines is always less than the energy input, even thoughthe forces may be drastically different.

Considering this, how do you calculate pulley output?

Attach a known mass to the other end of the cord. Itwill be necessary to determine force when you want to**calculate** the **work** input in a **pulley** or asystem of **pulleys**. **Work** is determined by multiplyingforce by distance traveled: **Work** = Force X Distance W=Fd.

How do you find the efficiency?

Since work is the change in kinetic energy, the**efficiency** of a machine can be stated as the percentage ofthe output work divided by the input work minus the work lost fromto friction and heat. Multiply Eff by 100% to **get theefficiency** percentage.