How Much Work Does a Machine Perform Between 9s and 18s?

In summary, the formula for calculating power is Power = Work / Time, where power is measured in watts (W), work is measured in joules (J), and time is measured in seconds (s). To determine the power output of a machine, you can use the formula Power = Force x Velocity, where power is measured in watts (W), force is measured in newtons (N), and velocity is measured in meters per second (m/s). Power and energy are closely related concepts, with power being the rate at which energy is transferred or used. AC (alternating current) and DC (direct current) are two types of electrical power, with AC alternating direction and DC maintaining a constant direction. To reduce power consumption, you
  • #1
pph1011
3
0

Homework Statement


A machine does work at a rate given by , P=ct^2 where c= 18 W/s^2 and t is time.
Find the work done by the machine between 9.0s and 18s .

Homework Equations



P=w/t

The Attempt at a Solution



no ideas
 
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  • #2


pph1011 said:

Homework Statement


A machine does work at a rate given by , P=ct^2 where c= 18 W/s^2 and t is time.
Find the work done by the machine between 9.0s and 18s .

Homework Equations



P=w/t

The Attempt at a Solution



no ideas

Integrate with respect to time because:

[tex]P=\frac{dW}{dt}[/tex].
 
  • #3


I would approach this problem by first acknowledging that the given equation, P=ct^2, represents the power of the machine, not the work done. Power is the rate at which work is done, so in order to find the work done by the machine, we must use the formula P=w/t, where P is power, w is work, and t is time.

Next, I would substitute the given values into the formula. Since we are looking for the work done between 9.0s and 18s, we can set t=9.0s and t=18s respectively. This gives us two equations:

P1 = w/9.0s
P2 = w/18s

Since we know that P=ct^2, we can substitute that into the equations:

P1 = c(9.0s)^2
P2 = c(18s)^2

Finally, we can substitute the given value for c (18 W/s^2) into the equations and solve for w:

P1 = (18 W/s^2)(9.0s)^2 = 1458 J
P2 = (18 W/s^2)(18s)^2 = 5832 J

Therefore, the work done by the machine between 9.0s and 18s is 5832 J - 1458 J = 4374 J.

In conclusion, by using the correct formula and substituting the given values, we can find the work done by the machine between 9.0s and 18s. This approach demonstrates the importance of understanding the difference between power and work and using the appropriate equations in problem solving.
 

FAQ: How Much Work Does a Machine Perform Between 9s and 18s?

What is the formula for calculating power?

The formula for calculating power is Power = Work / Time, where power is measured in watts (W), work is measured in joules (J), and time is measured in seconds (s).

How do I determine the power output of a machine?

To determine the power output of a machine, you can use the formula Power = Force x Velocity, where power is measured in watts (W), force is measured in newtons (N), and velocity is measured in meters per second (m/s). This formula is commonly used for calculating the power output of engines and motors.

How does power relate to energy?

Power and energy are closely related concepts. Power is the rate at which energy is transferred or used, while energy is the capacity to do work. In other words, power is the amount of energy used per unit of time. The unit of energy is the joule (J), and the unit of power is the watt (W).

What is the difference between AC and DC power?

AC (alternating current) and DC (direct current) are two types of electrical power. AC power is generated by power plants and alternates direction at a specific frequency, usually 60 cycles per second in the US. DC power, on the other hand, maintains a constant direction and is commonly used in batteries and electronic devices.

How can I reduce my power consumption?

There are several ways to reduce your power consumption, such as turning off lights and electronics when not in use, using energy-efficient appliances and LED light bulbs, and adjusting your thermostat to save energy. Conserving energy not only reduces your power usage, but it also helps save money and protect the environment.

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