An acrobat hangs from a trapeze with the tension in both ropes is 315 Newtons.What is the mass of the acrobat?
Hmmmm.
on the trapeze, if it is still, hanging downward, mass*9.8=2*315
solve for msss
one the second, each side is holding half the weight.
(1/2 * 87.9*9.8)/tension= sin10.1deg
solve for tension.
M*g = 87.9 * 9.8 = 861.4 N. = Wt. of acrobat.
All angles are referenced to +x-axis.
T1*sin(180-10.1) + T2*sin(10.1) = 861.4.
0.1754T1 + 0.1754T2 = 861.4
T2 = T1
0.1754T1 + 0.1754T1 = 861.4
0.3507T1 = 861.4
T1 = 2456 N. = T2.
To find the mass of the acrobat, we can use the equation F = mg, where F is the force (tension in the ropes), m is the mass, and g is the acceleration due to gravity.
Given that the tension in both ropes is 315 Newtons, we can set up the equation as follows:
315 = m * g
To solve for the mass, we need to know the acceleration due to gravity. On Earth, the standard acceleration due to gravity is approximately 9.8 m/s^2. Let's assume that value for this calculation.
315 = m * 9.8
Now, we can solve for the mass (m):
m = 315 / 9.8 ≈ 32.14 kg
Therefore, the mass of the acrobat is approximately 32.14 kilograms.