Pre calculus HW

Question

A 75-Ib weight hangs from a string as shown in the figure. Find the tensions T1 and T2 in the string. (Round your answers to one decimal place.) T1 is 50 degrees and T2 is 30 degrees.

Answer 1

Unfortunately, there is no figure attached to the question. However, i can provide a general explanation of how to solve the problem.

To find the tensions T1 and T2 in the string, we need to consider the forces acting on the weight. There are two tension forces acting on the weight: T1 and T2. The weight is also subject to the force of gravity, which acts vertically downwards.

We can use the fact that the weight is in equilibrium, meaning that the net force acting on it is zero. This means that the vector sum of the forces acting on the weight must be zero. We can break the forces down into their horizontal and vertical components and write two equations, one for each direction:

Vertical direction: T1sin(50°) + T2sin(30°) - mg = 0

Horizontal direction: T1cos(50°) - T2cos(30°) = 0

In these equations, m is the mass of the weight (converted to pounds) and g is the acceleration due to gravity (32.2 ft/s^2). We can substitute these values and solve for T1 and T2:

T1 = (mg - T2sin(30°)) / sin(50°) T2 = (T1cos(50°)) / cos(30°)

Substituting the given values (m=75 lbs) and using the conversion factor 1 lb = 4.45 N, we get:

T1 = (75 lbs x 4.45 N/lb - T2sin(30°)) / sin(50°) = 190.6 N - T2sin(30°) / 0.766 T2 = (T1cos(50°)) / cos(30°) = 123.8 N

To find T2sin(30°), we can use the equation T2cos(30°) = T1cos(50°) and solve for T2sin(30°):

T2cos(30°) = T1cos(50°) T2sin(30°) = T1sin(50°) x (cos(30°) / sin(30°)) T2sin(30°) = T1sin(50°) x 0.577

Substituting this expression into the equation for T1, we get:

T1 = (75 lbs x 4.45 N/lb - T2sin(30°)) / sin(50°) T1 = (333.8 N - 0.577 T1sin(50°)) / 0.766 T1 = 342.3 N

Now we can substitute T1 into the equation for T2 to get the final answer:

T2 = (T1cos(50°)) / cos(30°) = 218.8 N

Therefore, the tensions T1 and T2 in the string are approximately 342.3 N and 218.8 N, respectively. Note that these values are rounded to one decimal place.