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How many joules of energy does a 100-watt light bulb use per hour? How fast would a 70 kg person have to run to have that amount of kinetic energy?

Short Answer

Expert verified
A 100-watt bulb uses 360,000 joules per hour. A 70 kg person must run at 101.42 m/s to match that energy in kinetic form.

Step by step solution

01

Convert Watts to Joules

To find how many joules the bulb uses per hour, we start with its power rating: 100 watts. Since 1 watt = 1 joule/second, a 100-watt bulb uses \(100 \text{ joules/second}\). To find the energy consumption in one hour, multiply by the number of seconds in an hour (3600):\[100 \text{ watts} \times 3600 \text{ seconds} = 360,000 \text{ joules}.\]
02

Kinetic Energy Formula

The kinetic energy \(E_k\) of an object is given by the formula \(E_k = \frac{1}{2}mv^2\), where \(m\) is mass and \(v\) is velocity. We need to find the velocity that gives a 70 kg person 360,000 joules of energy.
03

Solve for Velocity

Rearrange the kinetic energy formula to solve for velocity \(v\): \[v = \sqrt{\frac{2E_k}{m}}.\] Substitute \(E_k = 360,000\) joules and \(m = 70\) kg: \[v = \sqrt{\frac{2 \times 360,000}{70}}.\] Calculate: \[v \approx \sqrt{10,285.71} \approx 101.42 \text{ m/s}.\]
04

Conclusion

A 70 kg person needs to run at approximately 101.42 meters per second to have 360,000 joules of kinetic energy, the same as the energy used by a 100-watt light bulb in one hour.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Energy Conversion
Energy conversion is the process of transforming energy from one form to another. In our exercise, we focus on converting electrical power, measured in watts, into energy, measured in joules. This is a common conversion since electrical appliances, like our 100-watt light bulb, have power ratings that help us understand their energy usage. Understanding energy conversion allows us to compare different forms of energy and see how they relate in practical applications.
Watts to Joules
Converting watts to joules can be straightforward once you know the basics. Watts measure power, which is the rate of energy use or generation. Joules, on the other hand, measure energy itself. One watt is equivalent to one joule per second.

To convert watts to joules for any duration, you multiply the watts by the number of seconds during which the energy flow is happening. So, in our example:
  • The light bulb is 100 watts, meaning it uses 100 joules every second.
  • There are 3600 seconds in an hour.
  • Therefore, in one hour, the bulb uses 100 watts × 3600 seconds, equating to 360,000 joules.
This practical conversion process is key for understanding energy consumption in everyday devices.
Mechanical Energy
Mechanical energy is the sum of kinetic and potential energy in an object related to its motion and position. In this exercise, we are mainly concerned with kinetic energy.

Kinetic energy is the energy possessed due to motion and can be calculated using the formula: \[ E_k = \frac{1}{2}mv^2 \]
  • \( m \) is mass
  • \( v \) is velocity.
In our scenario with the person running, we focus entirely on kinetic energy to achieve the equivalent of the light bulb's energy. The more massive or faster an object, the greater its kinetic energy.

Understanding mechanical energy helps us appreciate how energy is harnessed and exerted, whether in machinery or living organisms.
Velocity Calculation
Calculation of velocity is essential when determining how fast an object must travel to possess a certain amount of kinetic energy. To solve for velocity in the context of kinetic energy, we rearrange the kinetic energy formula:\[ v = \sqrt{\frac{2E_k}{m}} \]In our exercise, \( E_k \) is 360,000 joules, and \( m \) is 70 kg.Substitute these values into the equation to find:\[ v = \sqrt{\frac{2 \times 360,000}{70}} \]This calculation gives us a velocity of approximately 101.42 meters per second.

This process shows how changes in kinetic energy reflect different speeds needed based on mass. It highlights the relationship between velocity and energy, illustrating that even small increases in speed can significantly impact energy in motion.

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Most popular questions from this chapter

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. When you push the platform, you compress the springs. You do 80.0 J of work when you compress the springs 0.200 m from their uncompressed length. (a) What magnitude of force must you apply to hold the platform in this position? (b) How much \(additional\) work must you do to move the platform 0.200 m \(farther\), and what maximum force must you apply?

A crate on a motorized cart starts from rest and moves with a constant eastward acceleration of \(a = 2.80 \, \mathrm{m/s}^2\). A worker assists the cart by pushing on the crate with a force that is eastward and has magnitude that depends on time according to \(F(t) = (5.40 \, \mathrm{N/s})t\). What is the instantaneous power supplied by this force at \(t = 5.00\) s?

On December 27, 2004, astronomers observed the greatest flash of light ever recorded from outside the solar system. It came from the highly magnetic neutron star SGR 1806-20 (a \(magnetar\)). During 0.20 s, this star released as much energy as our sun does in 250,000 years. If \(P\) is the average power output of our sun, what was the average power output (in terms of \(P\)) of this magnetar?

A sled with mass 12.00 kg moves in a straight line on a frictionless, horizontal surface. At one point in its path, its speed is 4.00 m/s; after it has traveled 2.50 m beyond this point, its speed is 6.00 m/s. Use the work\(-\)energy theorem to find the force acting on the sled, assuming that this force is constant and that it acts in the direction of the sled's motion.

When a car is hit from behind, its passengers undergo sudden forward acceleration, which can cause a severe neck injury known as \(whiplash\). During normal acceleration, the neck muscles play a large role in accelerating the head so that the bones are not injured. But during a very sudden acceleration, the muscles do not react immediately because they are flexible; most of the accelerating force is provided by the neck bones. Experiments have shown that these bones will fracture if they absorb more than 8.0 J of energy. (a) If a car waiting at a stoplight is rear-ended in a collision that lasts for 10.0 ms, what is the greatest speed this car and its driver can reach without breaking neck bones if the driver's head has a mass of 5.0 kg (which is about right for a 70-kg person)? Express your answer in m/s and in mi/h. (b) What is the acceleration of the passengers during the collision in part (a), and how large a force is acting to accelerate their heads? Express the acceleration in m/s\(^2\) and in \(g\)'s.

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