Mixing
How to solve this vector problem involving more than one unknown?
$begingroup$
This is an exercise I came across while tutoring high school physics. I am posting this as an "answer my own question."
Kyle suspends a 12340 N moose from two trees as shown below. What is the tension in the rope on the right?
The answer is shown below.
algebra-precalculus trigonometry euclidean-geometry physics
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
add a comment |
$begingroup$
This is an exercise I came across while tutoring high school physics. I am posting this as an "answer my own question."
Kyle suspends a 12340 N moose from two trees as shown below. What is the tension in the rope on the right?
The answer is shown below.
algebra-precalculus trigonometry euclidean-geometry physics
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
3
$begingroup$
Does your country have any animal cruelty legislation?
$endgroup$
– Lord Shark the Unknown
Jan 20 at 6:57
2
$begingroup$
We have lots of moose. And no moose were harmed in the framing of this question.
$endgroup$
– Adam Hrankowski
Jan 20 at 8:15
add a comment |
$begingroup$
This is an exercise I came across while tutoring high school physics. I am posting this as an "answer my own question."
Kyle suspends a 12340 N moose from two trees as shown below. What is the tension in the rope on the right?
The answer is shown below.
algebra-precalculus trigonometry euclidean-geometry physics
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
This is an exercise I came across while tutoring high school physics. I am posting this as an "answer my own question."
Kyle suspends a 12340 N moose from two trees as shown below. What is the tension in the rope on the right?
The answer is shown below.
algebra-precalculus trigonometry euclidean-geometry physics
algebra-precalculus trigonometry euclidean-geometry physics
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
asked Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
2,094930
3
$begingroup$
Does your country have any animal cruelty legislation?
$endgroup$
– Lord Shark the Unknown
Jan 20 at 6:57
2
$begingroup$
We have lots of moose. And no moose were harmed in the framing of this question.
$endgroup$
– Adam Hrankowski
Jan 20 at 8:15
add a comment |
3
$begingroup$
Does your country have any animal cruelty legislation?
$endgroup$
– Lord Shark the Unknown
Jan 20 at 6:57
2
$begingroup$
We have lots of moose. And no moose were harmed in the framing of this question.
$endgroup$
– Adam Hrankowski
Jan 20 at 8:15
3
3
$begingroup$
Does your country have any animal cruelty legislation?
$endgroup$
– Lord Shark the Unknown
Jan 20 at 6:57
$begingroup$
Does your country have any animal cruelty legislation?
$endgroup$
– Lord Shark the Unknown
Jan 20 at 6:57
2
2
$begingroup$
We have lots of moose. And no moose were harmed in the framing of this question.
$endgroup$
– Adam Hrankowski
Jan 20 at 8:15
$begingroup$
We have lots of moose. And no moose were harmed in the framing of this question.
$endgroup$
– Adam Hrankowski
Jan 20 at 8:15
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Here is a clip from my notebook:
There are three forces in equilibrium acting on the moose: It's weight of $12340 N$, and the tensions on the ropes, $T_L$ and $T_R$. The horizontal and vertical components of the tensions are also shown.
Since the body is in equilibrium, the net force is zero. All notation refers to the magnitudes of the vectors. Angles are in degrees. Forces and Tensions are in Newtons
The left and right horizontal forces are equal in magnitude:
$$F_H = T_R cos 64 = T_L cos 41$$
The sum of the upward vertical forces equal the magnitude of the downward vertical force:
$$F_UR + F_UL = 12340$$
Combining terms to solve for $T_R$:
$$F_UR = T_R sin 64 $$
$$F_UL = T_L sin 41 $$
Therefore:
$$T_R sin 64 + T_L sin 41 = 12340$$
$$T_R sin 64 + (frac {F_H}{ cos 41})sin 41 = 12340$$
$$T_R sin 64 + (frac {T_R cos 64}{ cos 41})sin 41 = 12340$$
$$T_R (sin 64 + (frac {cos 64}{ cos 41})sin 41) = 12340$$
Finally:
$$T_R = frac{12340}{sin 64 + (frac {cos 64}{ cos 41})sin 41}$$
$$T_R approx 9641.65 $$
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Here is a clip from my notebook:
There are three forces in equilibrium acting on the moose: It's weight of $12340 N$, and the tensions on the ropes, $T_L$ and $T_R$. The horizontal and vertical components of the tensions are also shown.
Since the body is in equilibrium, the net force is zero. All notation refers to the magnitudes of the vectors. Angles are in degrees. Forces and Tensions are in Newtons
The left and right horizontal forces are equal in magnitude:
$$F_H = T_R cos 64 = T_L cos 41$$
The sum of the upward vertical forces equal the magnitude of the downward vertical force:
$$F_UR + F_UL = 12340$$
Combining terms to solve for $T_R$:
$$F_UR = T_R sin 64 $$
$$F_UL = T_L sin 41 $$
Therefore:
$$T_R sin 64 + T_L sin 41 = 12340$$
$$T_R sin 64 + (frac {F_H}{ cos 41})sin 41 = 12340$$
$$T_R sin 64 + (frac {T_R cos 64}{ cos 41})sin 41 = 12340$$
$$T_R (sin 64 + (frac {cos 64}{ cos 41})sin 41) = 12340$$
Finally:
$$T_R = frac{12340}{sin 64 + (frac {cos 64}{ cos 41})sin 41}$$
$$T_R approx 9641.65 $$
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
add a comment |
$begingroup$
Here is a clip from my notebook:
There are three forces in equilibrium acting on the moose: It's weight of $12340 N$, and the tensions on the ropes, $T_L$ and $T_R$. The horizontal and vertical components of the tensions are also shown.
Since the body is in equilibrium, the net force is zero. All notation refers to the magnitudes of the vectors. Angles are in degrees. Forces and Tensions are in Newtons
The left and right horizontal forces are equal in magnitude:
$$F_H = T_R cos 64 = T_L cos 41$$
The sum of the upward vertical forces equal the magnitude of the downward vertical force:
$$F_UR + F_UL = 12340$$
Combining terms to solve for $T_R$:
$$F_UR = T_R sin 64 $$
$$F_UL = T_L sin 41 $$
Therefore:
$$T_R sin 64 + T_L sin 41 = 12340$$
$$T_R sin 64 + (frac {F_H}{ cos 41})sin 41 = 12340$$
$$T_R sin 64 + (frac {T_R cos 64}{ cos 41})sin 41 = 12340$$
$$T_R (sin 64 + (frac {cos 64}{ cos 41})sin 41) = 12340$$
Finally:
$$T_R = frac{12340}{sin 64 + (frac {cos 64}{ cos 41})sin 41}$$
$$T_R approx 9641.65 $$
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
add a comment |
$begingroup$
Here is a clip from my notebook:
There are three forces in equilibrium acting on the moose: It's weight of $12340 N$, and the tensions on the ropes, $T_L$ and $T_R$. The horizontal and vertical components of the tensions are also shown.
Since the body is in equilibrium, the net force is zero. All notation refers to the magnitudes of the vectors. Angles are in degrees. Forces and Tensions are in Newtons
The left and right horizontal forces are equal in magnitude:
$$F_H = T_R cos 64 = T_L cos 41$$
The sum of the upward vertical forces equal the magnitude of the downward vertical force:
$$F_UR + F_UL = 12340$$
Combining terms to solve for $T_R$:
$$F_UR = T_R sin 64 $$
$$F_UL = T_L sin 41 $$
Therefore:
$$T_R sin 64 + T_L sin 41 = 12340$$
$$T_R sin 64 + (frac {F_H}{ cos 41})sin 41 = 12340$$
$$T_R sin 64 + (frac {T_R cos 64}{ cos 41})sin 41 = 12340$$
$$T_R (sin 64 + (frac {cos 64}{ cos 41})sin 41) = 12340$$
Finally:
$$T_R = frac{12340}{sin 64 + (frac {cos 64}{ cos 41})sin 41}$$
$$T_R approx 9641.65 $$
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
$endgroup$
Here is a clip from my notebook:
There are three forces in equilibrium acting on the moose: It's weight of $12340 N$, and the tensions on the ropes, $T_L$ and $T_R$. The horizontal and vertical components of the tensions are also shown.
Since the body is in equilibrium, the net force is zero. All notation refers to the magnitudes of the vectors. Angles are in degrees. Forces and Tensions are in Newtons
The left and right horizontal forces are equal in magnitude:
$$F_H = T_R cos 64 = T_L cos 41$$
The sum of the upward vertical forces equal the magnitude of the downward vertical force:
$$F_UR + F_UL = 12340$$
Combining terms to solve for $T_R$:
$$F_UR = T_R sin 64 $$
$$F_UL = T_L sin 41 $$
Therefore:
$$T_R sin 64 + T_L sin 41 = 12340$$
$$T_R sin 64 + (frac {F_H}{ cos 41})sin 41 = 12340$$
$$T_R sin 64 + (frac {T_R cos 64}{ cos 41})sin 41 = 12340$$
$$T_R (sin 64 + (frac {cos 64}{ cos 41})sin 41) = 12340$$
Finally:
$$T_R = frac{12340}{sin 64 + (frac {cos 64}{ cos 41})sin 41}$$
$$T_R approx 9641.65 $$
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
answered Jan 20 at 6:39
Adam HrankowskiAdam Hrankowski
2,094930
2,094930
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
add a comment |
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
$begingroup$
What you have done is correct? By the bye, what is your question?
$endgroup$
– Satish Ramanathan
Jan 20 at 6:58
add a comment |
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3
$begingroup$
Does your country have any animal cruelty legislation?
$endgroup$
– Lord Shark the Unknown
Jan 20 at 6:57
2
$begingroup$
We have lots of moose. And no moose were harmed in the framing of this question.
$endgroup$
– Adam Hrankowski
Jan 20 at 8:15