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 tension in the cable (T), the horizontal component of the force on the strut from the hinge, and the vertical component of the force on the strut from the hinge, we can use the principles of equilibrium.
(a) To find the tension in the cable (T), we can start by drawing a free body diagram of the system. The diagram should include the strut, the concrete block, the hinge, and the forces acting on each of them.
In this case, the forces acting on the strut are:
- The tension in the cable (T)
- The force from the hinge (F_hinge) with both horizontal and vertical components
The forces acting on the concrete block are:
- The tension in the cable (T)
- The force of gravity (m_block * g), where m_block is the mass of the block and g is the acceleration due to gravity
Since the system is in equilibrium, the sum of the forces in both the horizontal and vertical directions should be zero.
In the horizontal direction, we have:
F_hinge_horizontal = T (since there are no other horizontal forces)
In the vertical direction, we have:
F_hinge_vertical - m_block * g = 0
To solve for T, we need to find the components of the force from the hinge. The horizontal component can be found using trigonometry:
F_hinge_horizontal = F_hinge * cos(ϕ)
The vertical component can also be found using trigonometry:
F_hinge_vertical = F_hinge * sin(ϕ)
Using the given angles, we have:
ϕ = 30.0°
è = 45.0°
To find the tension (T), we can plug these values into the equations and solve them simultaneously.