I explained part of the solution with the question, but stilll lost to find the
ID: 1323520 • Letter: I
Question
I explained part of the solution with the question, but stilll lost to find the theta. Please help and make sure to include your solution with explanation
Since the angle theta is now expressed in terms of known properties, you can find the tension T in the rope. To find the distance w, use the Pythagorean theorem on the red triangle in the figure and use the blue triangle to relate the distance h to the dimensions S, H, and W. You can calculate the tension in the rope by considering the pulley as the system. Since the system is in equilibrium (that is, the pulley is not accelerating in any direction, then you can use Newton?s second law to determine the relationship between the tension in the rope and the angle subtended by the rope, as shown to the right. Therefore, sum the forces acting in the horizontal direction and do the same for the vertical direction. Noting that the tension is the same throughout the rope, you should be able to show that 9 4and that T= ing 2sin(9), the geometry of the problem simplifies, as shown on the right. Here, S is the length of the rope, W is the distance between crossing points, and H is the difference in heights between the crossing points. By reflecting the line segment denoted h in the figure below the horizontal dashed line, you should be able to one or more trigonometric identities and the Pythagorean theorem to determine fundamental relationships between W, S, and H and the angle 9. (See third figure below). Most importantly, you should be able to As a stunt coordinator with a background in physics, you have been asked to determine whether Bear can make it across the river and whether the rope will hold his weight. Bear is rather small, with a mass of only about 43.5 kg, including his equipment. The crossing distance is roughly W 7.7 m and the rope is tied H = 1.5 m lower on the opposing the bank. Judging by the sag in the rope, its length is about 11.7 m. Calculate the tension in the rope once Bear reaches a point of equilibrium. Assume the rope does not stretch Number If Bear can make it far enough across (at least 5.4 m from where he starts), he can drop down onto the river bank below. How far will he travel across?Explanation / Answer
Note that
S = length of the rope = 11.7 m
W = end to end width = 7.7 m
As
theta = Arcsin {sqrt[(S^2 - W^2)/S]
Plugging these data in,
theta = 48.84 degrees
Thus, as
T = mg/[2sin(theta)]
where
m = 43.5 kg
g = 9.8 m/s^2
Then
T = 283 N [ANSWER]
DONE!
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