(ii) Calculate the direction and magnitude of the joint force at the mid-point between the fourth and fifth lumbar vertebrae by considering the forces and moments acting on the lower body.
Direction of joint force at midpoint between L4 and L5 = F =?
ILB lower body mass moment arm = 15cm
WLB Lower body weight = 370N
Weight moment arm = IW = 35 cm
W uB upper body weight = 430 N
L uB Upper body mass moment arm =15 cm
LlB lower body mass moment arm=15cm
lw weight moment arm =35cm
muscle force moment arm =50mm
trunk angle 40 degree with the vertical
To calculate the direction and magnitude of the joint force at the mid-point between the fourth and fifth lumbar vertebrae, we need to consider the forces and moments acting on the lower body.
1. Calculate the horizontal and vertical components of the lower body weight (WLB) using the angle of the trunk with the vertical (40 degrees):
Horizontal component: WLB_horizontal = WLB * sin(trunk angle)
Vertical component: WLB_vertical = WLB * cos(trunk angle)
2. Calculate the moments due to the lower body weight and upper body weight around the mid-point of L4 and L5:
Moment due to lower body weight (MLB) = WLB_horizontal * ILB
Moment due to upper body weight (MUB) = WUB * LUW
3. Calculate the muscle force (FM) using the moment arm (rM) and moment due to the upper body weight:
FM = MUB / rM
Note: The moment arm for the muscle force (rM) is given as 50mm, so you may need to convert it to meters for consistency.
4. Calculate the resultant force (F) at the mid-point between L4 and L5:
Horizontal component of F: F_horizontal = WLB_horizontal
Vertical component of F: F_vertical = -WLB_vertical - FM
Since we have the horizontal and vertical components of the resultant force, we can calculate the magnitude of the resultant force (F) as:
Magnitude of F: |F| = sqrt(F_horizontal^2 + F_vertical^2)
To determine the direction of the joint force, you can use the angle of the resultant force with the horizontal axis. This can be calculated using the arctan of the vertical component divided by the horizontal component:
Direction of joint force: Angle = atan(F_vertical / F_horizontal)
By following these steps and plugging in the appropriate values for the variables given in the problem (e.g., ILB, WLB, WUB, LUW, rM), you should be able to calculate the direction and magnitude of the joint force at the midpoint between L4 and L5.
To calculate the direction and magnitude of the joint force at the mid-point between the fourth and fifth lumbar vertebrae, we need to consider the forces and moments acting on the lower body.
Let's break down the steps:
Step 1: Calculate the weight moment of the lower body.
Weight moment of the lower body (IW) = WLB * lw
where WLB is the lower body weight (370N) and lw is the weight moment arm (35cm).
IW = 370N * 35cm = 12950 N*cm
Step 2: Calculate the weight moment of the upper body.
Weight moment of the upper body (IWuB) = W uB * lb
where W uB is the upper body weight (430N) and lb is the weight moment arm (35cm).
IWuB = 430N * 35cm = 15050 N*cm
Step 3: Calculate the muscle force moment.
Muscle force moment (IMF) = MF * lm
where MF is the muscle force and lm is the muscle force moment arm (50mm). Convert the muscle force moment arm from mm to cm: 50mm = 5cm.
IMF = MF * 5cm
Step 4: Calculate the net moment on the mid-point between L4 and L5.
Net moment = IW + IWuB - IMF
Step 5: Calculate the magnitude of the joint force.
Magnitude of the joint force (F) = Net moment / ILB
where ILB is the lower body mass moment arm (15cm).
F = Net moment / 15cm
Step 6: Calculate the direction of the joint force.
To find the direction of the joint force, we need to consider the trunk angle of 40 degrees with the vertical. Since no specific information is given about the direction of the forces, we assume that all forces are acting vertically. Therefore, the direction of the joint force would be upward.
Put all the values into the equations and compute the results.