A copper rod 81 cm long is used to poke a fire. the hot end of the rod is maintained at 105° c and the cool end has a constant t
1 answer:
The temperature inside the copper rod varies linearly with the distance from the hot end of the rod. This means that we can find the temperature at 23 cm (let's call it 'point A') from the cool end by solving a linear proportion.
The temperature difference between the two ends of the rod is
and this corresponds to a length of 81 cm. Therefore, we can write:
from which we find
This is not the final answer actually; this is the temperature difference between the cool end and point A. So, the temperature at point A is
The temperature difference between the two ends of the rod is
and this corresponds to a length of 81 cm. Therefore, we can write:
from which we find
This is not the final answer actually; this is the temperature difference between the cool end and point A. So, the temperature at point A is
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Let's use the mirror equation to solve the problem:
where f is the focal length of the mirror,
the distance of the object from the mirror, and 
the distance of the image from the mirror.
For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for by using the numbers given in the text of the problem:
Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.
where f is the focal length of the mirror,
For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for
Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.
a) See graph in attachment
b) The suvat equation to use is
c) The acceleration is
d) The acceleration is
e) The time needed is 8 s
Explanation:
a)
For this part, find in attachment the diagram representing this situation.
Since we are not given any particular direction for the motion, we choose the x-direction as the direction of motion of the boat.
Then we have the following:
- The initial position of the boat is , the origin
- The final position of the boat is
- The initial velocity of the boat is
- The final velocity of the boat is
Note that the arrow representing the final velocity is longer than that of the initial velocity, since the final velocity is larger.
b)
The motion of the speed boat is a uniformly accelerated motion (motion at constant acceleration), therefore we can use one of the suvat equations. In this particular problem, we know the following quantities:
, the initial velocity
, the final velocity
, the displacement of the boat
Therefore, the equation that best can be use to find the acceleration is
where
is the acceleration
c)
Now we have to solve the equation
In order to find the acceleration.
This can be done by dividing both terms by : this way, we find
And so the acceleration is
d)
Now we can use the equation found in part c) in order to find the acceleration.
We have the following data:
, the initial velocity
, the final velocity
, the displacement of the boat
And substituting into the equation,
e)
In order to find the time it takes the boat to travel the given distance, we can use the following suvat equation:
where:
is the initial velocity
is the final velocity
a is the acceleration
t is the time
Here we have:
Solving for t, we find:
Learn more about accelerated motion:
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