A concrete block of mass 244 kg hangs from the end of the uniform strut of mass 45.0 kg. Angle ϕ = 30.0° and è = 45.0°.

(a) Find the tension T in the cable.
N

(b) Find the horizontal component of the force on the strut from the hinge.
N (right)

(c) Find the vertical component of the force on the strut from the hinge.
N (up)

To find the answers to these questions, we can use the principles of equilibrium and analyze the forces acting on the system.

(a) Find the tension T in the cable:

The tension T in the cable can be found by considering the forces acting on the concrete block.

First, we need to resolve the weight of the block into its vertical and horizontal components. The vertical component is given by:

Weight_vertical = mass_block * g * cos(φ) --- (1)

where mass_block is the mass of the concrete block, g is the acceleration due to gravity, and φ is the angle between the strut and the vertical.

The horizontal component can be calculated as:

Weight_horizontal = mass_block * g * sin(φ) --- (2)

Next, we need to consider the forces acting along the strut. There are two forces acting on it: the tension T in the cable and the force from the hinge.

Since the system is in equilibrium, the sum of the forces along the strut in the horizontal direction must be zero:

Horizontal_force_strut = T * cos(è) - Weight_horizontal = 0 --- (3)

Similarly, in the vertical direction, the sum of the forces must be zero:

Vertical_force_strut = T * sin(è) + Weight_vertical = 0 --- (4)

We now have two equations (3) and (4) with two unknowns (T and Weight_horizontal/vertical). We can solve them simultaneously to find the tension T in the cable.

(b) Find the horizontal component of the force on the strut from the hinge:

Using the equation (3) from the previous part, we can solve for the horizontal component of the force on the strut from the hinge. The expression T * cos(è) gives the horizontal component, and the direction can be determined based on the sign of the force.

(c) Find the vertical component of the force on the strut from the hinge:

Similarly, using equation (4) from the previous part, we can solve for the vertical component of the force on the strut from the hinge. The expression T * sin(è) gives the vertical component, and the direction can be determined based on the sign of the force.

By solving the equations and plugging in the given values for mass_block, mass_strut, and the angles φ and è, you can find the numerical values for the tension T in the cable, as well as the horizontal and vertical components of the force on the strut from the hinge.