The question is: Is the easier solution more accurate than the previous one?

[Craig113]

Hello people, pardon my poor grammar and my horrible spelling. Let my make it clear to all that in not looking for someone to do my homework. I just need a push on the right direction.
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a ball with the mass of 50 grams hangs on a very light thread who has the length of 80 cm and swing back and forth (pendel). At the beginning of the movement the maximum angle that the thread formed when moving was 35 degress, but after one minute tha angle had declined to 2o degress.The time for the ball to make one swing from its lowest point to its highest remained the same.

The question is: Is the power that the swinging energi (mekanic energi) from the pendel turns into other energi forms under one minute bigger or smaller than the averge power of the pendel?

Solution:

Well, i know how to calculate the power that turns the mekanic energi to other energiforms, its very easy. Power is P = delta E/ delta t
How much energi has the pendel lost under one minute? Tha answer to that question be found by comparing the highest level of potential energy for 35 and 20 degress. To do that you need to calculate how high the ball went from its lowest when de turning angle was 20 degress and 35 degress. That is easy to, just use basic trigonametry. When you have calculated the energ lost under one minute, get the power by using the formula P =E/60.

But as i understand it, the "average power" of the pendel is the energi amout
that turn from one form to another while the pendel swings one time from its highest point over ground to its lowest divided with the time it takes to preform the movement. To calculate this one must first calculate the speed of the pendel at the angles, divid the speed with 2, to get averege speed. ne must calculate the distance that the pendel travels by using the formula
(r*2 pi)/360 * 20 or 35. And calculate the time by dividing the distance with the average speed. When you have the time t you can calculate the power of the pendel for 20 and 35 degress. And finally calculate the "average power" of the pendel by adding the to powers for 29 and 35 degress and dividing them with two.
I have done all this, and my answer is that the average power of the pendel is much higher than the power that turns the pendels mekanic energi to other energiforms, why am i wrong? Its insane.



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A mousetrap is used as a engine for a small car with the mass of 50 gram.The car mus be able to travel 8 meters. the mousetraps arm is about 4 cm, and it can be pulled 180 degress. The force needed to pull the arm of the mousetrap is linear dependable to the turning angle. its at its lowest point 2 N and on its highest about 10 Newton.

the question is: What it the maximum violocity this car can have?

Solution: The road that the "car" must travel is not of any importance.
the most important thing is to calculate how much energi can be feed into the spring of the mousetrap. You can get the violocity when you get the total energy by the formula E = 0.5 *mv^2. The distance/displacement you have to use a force F to "cock the spring" is given by a half circle, you get that by the formula 2*0.04*pi/2. The force you have to use depends of the angle. The energi used is A= F*s. Its in this case the same as the area of a
triangle with the hight 8 Newton and the length of ( 2*0.04*pi/2). This calculation should give one the energi feed into the mousetrap spring?
And with the energi you can calculate the maximum speed.
am i wrong? Why then?

 

[Craig113]

Why is nobody answering? Dont understand, have done something that against the rulez?

 

[whozum]

The question is: Is the power that the swinging energi (mekanic energi) from the pendel turns into other energi forms under one minute bigger or smaller than the averge power of the pendel?

The power lost due to friction is the change in PE at the peaks (or KE at the bottom) of each swing. I don't think that's what you were getting at above.

The average power of the pendulum would be the work done by the pendulum divided by the time period its done it in. Kind of ambiguous question if you ask me.

 

[geosonel]

A mousetrap is used as a engine for a small car with the mass of 50 gram.The car mus be able to travel 8 meters. the mousetraps arm is about 4 cm, and it can be pulled 180 degress. The force needed to pull the arm of the mousetrap is linear dependable to the turning angle. its at its lowest point 2 N and on its highest about 10 Newton.

the question is: What it the maximum violocity this car can have?

Solution: The road that the "car" must travel is not of any importance.
the most important thing is to calculate how much energi can be feed into the spring of the mousetrap. You can get the violocity when you get the total energy by the formula E = 0.5 *mv^2. The distance/displacement you have to use a force F to "cock the spring" is given by a half circle, you get that by the formula 2*0.04*pi/2. The force you have to use depends of the angle. The energi used is A= F*s. Its in this case the same as the area of a
triangle with the hight 8 Newton and the length of ( 2*0.04*pi/2). This calculation should give one the energi feed into the mousetrap spring?
And with the energi you can calculate the maximum speed.
am i wrong? Why then?

KE transferred to car = (1/2)mv² = Energy from mousetrap = E

mousetrap force = F(θ) = (2 Newtons) + { (8 Newtons)*(θ/π) }
θ from 0 to π radians
F(θ) from 2 to 10 Newtons

$$E \ = \ \int F \, ds \ = \ \int_{0}^{\pi} F \, r \cdot d\theta \ = \ \int_{0}^{\pi} \left ( 2 \, + \, 8 \frac {\theta}{\pi} \right ) \, (0.04) \cdot d\theta \ = \ \left [ (2)(0.04) \theta \, + \, (8)(0.04) \frac {\theta^2}{2 \pi} \right ]_{0}^{\pi}$$

$$E \ = \ (2)(0.04) \pi \ + \ \frac {(8)(0.04) \pi}{2} \qquad \mbox{ = energy stored in mousetrap and delivered to car}$$

complete calculations & calculate velocity

 

[Craig113]

The power lost due to friction is the change in PE at the peaks (or KE at the bottom) of each swing. I don't think that's what you were getting at above.

The power of the pendulum yes.


The average power of the pendulum would be the work done by the pendulum divided by the time period its done it in. Kind of ambiguous question if you ask me.

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Dear friend, i first thought that "The average power" ot the pendulum and the Power that turns the energi of the pendulum to other energy forms where two different powers. And yes, one can argue that they are. But in this problem the "average power" is meant the average power that turns the total energy of the pendulum to other energi forms. So the question is really: is the power that turns the energy of the pendulum to other energy form under one minute higher or lower than the power that turns the total energy of the pendulum to other energy forms? And the answer is:

the power that turns the pendels energy to other energy forms under one minute is higher.
The reason is that while the pendulum losses energy and speed, the ball of the pendulum travels less distance and is exposed to less friction and stopping power from the air, thus lossing less energy is lost after eatch swing to friction and air, and the pendulum losses less hight and speed, still the time of eatch swing is the same, that means less power. Thus the average power that turns the total energy of the pendulum to other energy forms is less than the same power under one minute. Meaning the lost of the pendulum energy to friction and air decline with every swing.

 

[Craig113]

KE transferred to car = (1/2)mv² = Energy from mousetrap = E

mousetrap force = F(θ) = (2 Newtons) + { (8 Newtons)*(θ/π) }
θ from 0 to π radians
F(θ) from 2 to 10 Newtons

$$E \ = \ \int F \, ds \ = \ \int_{0}^{\pi} F \, r \cdot d\theta \ = \ \int_{0}^{\pi} \left ( 2 \, + \, 8 \frac {\theta}{\pi} \right ) \, (0.04) \cdot d\theta \ = \ \left [ (2)(0.04) \theta \, + \, (8)(0.04) \frac {\theta^2}{2 \pi} \right ]_{0}^{\pi}$$

$$E \ = \ (2)(0.04) \pi \ + \ \frac {(8)(0.04) \pi}{2} \qquad \mbox{ = energy stored in mousetrap and delivered to car}$$

complete calculations & calculate velocity

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im don't get it. Its the right answer though.
This problem is at a level that don't require knowledge about integrals first of.
And second i don't understand this integral, you can't use 0 and pi as the integrals limits, why? because you don't use the force f to do the displacement o to pi. And how can the factor 8 be in integral? You don't cock the spring 8 meters do you?

 

[Craig113]

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im don't get it. Its the right answer though.
This problem is at a level that don't require knowledge about integrals first of.
And second i don't understand this integral, you can't use 0 and pi as the integrals limits, why? because you don't use the force f to do the displacement o to pi. And how can the factor 8 be in integral? You don't cock the spring 8 meters do you?

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I think i found a easier solution, but its still thanks to you.

The force needed for a displacement is as you earlier
said F = (2 + (8*(r/pi)), and the work and energy feeded in the
spring is A= (F*s), s can be calculated easily as its a half circle,
(0.04 * 2 * pi)/2= 0.12566...
To calculate the total work, we need an integral that uses the limit 0 to 0.12566.. and still can calculate the force needed to make the displacement with x as the displacement, but the formula F= (2 + (8*(r/pi)) uses the angel to do so. But it the angel is dependable to the displacement as follow

(s/0.12566) * pi = angle, from this we get the F= 2 + 8 * ((s/0,12566)*pi)/pi
or put more simple F= 2 + 8* (s/0,12566..), this formula can be used in one integral with the lower limit 0 and the upper 0,12566. and you get the full energi of the spring.

 

[geosonel]

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I think i found a easier solution, but its still thanks to you.

The force needed for a displacement is as you earlier
said F = (2 + (8*(r/pi)), and the work and energy feeded in the
spring is A= (F*s), s can be calculated easily as its a half circle,
(0.04 * 2 * pi)/2= 0.12566...
To calculate the total work, we need an integral that uses the limit 0 to 0.12566.. and still can calculate the force needed to make the displacement with x as the displacement, but the formula F= (2 + (8*(r/pi)) uses the angel to do so. But it the angel is dependable to the displacement as follow

(s/0.12566) * pi = angle, from this we get the F= 2 + 8 * ((s/0,12566)*pi)/pi
or put more simple F= 2 + 8* (s/0,12566..), this formula can be used in one integral with the lower limit 0 and the upper 0,12566. and you get the full energi of the spring.

good work!