The hatchback of a car is positioned as shown to help determine the appropriate size for a damping
(a)
(b)
Fig. P16.134
(a)
The initial angular acceleration of the door.
Answer to Problem 16.134P
The initial angular acceleration of the door is
Explanation of Solution
Given information:
The weight of the door is
The mass moment of inertia of the center of gravity is
Calculation:
Consider the acceleration due to gravity as
Calculate the mass
Substitute
Sketch the Free Body Diagram of the door as shown in Figure 1.
Refer to Figure 1.
Calculate the distance
Calculate the distance
Calculate the position vectors as shown below.
The position of F with respect to H.
The position of E with respect to F.
Substitute
The position of E with respect to D.
The position of G with respect to E.
Apply the Equations of Equilibrium as shown below.
Apply the Equilibrium of forces along x direction as shown below.
Substitute
Apply the Equilibrium of forces along y direction as shown below.
Substitute
Substitute
Apply the Equilibrium of moment about G as shown below.
Calculate the acceleration at F
Substitute
Calculate the acceleration at E
Substitute
Calculate the acceleration at E
Substitute
Equating Equations (4) and (5) as shown below.
Resolving i and j components as shown below.
For i component.
For j component.
Calculate the relative acceleration
Substitute
Resolving i and j components as shown below.
For i component.
For j component.
Calculate the force at F
Substitute
Substitute
Calculate the force at E
Substitute
Substitute
Calculate the angular acceleration
Substitute
Therefore, the initial angular acceleration of the door is
(b)
The force on link FH.
Answer to Problem 16.134P
The force on link FH is
Explanation of Solution
Given information:
The weight of the door is
The mass moment of inertia of the center of gravity is
Calculation:
Refer to part (a).
The initial angular acceleration of the door is
Calculate the force at F
Substitute
Therefore, the force on link FH is
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