1
Name
MECH 223 – Engineering Statics
Final Exam, May 4th 2015
Question 1 (20 + 5 points)
(a) (8 points) Complete the following table
Force System Free Body Diagram EEs satisfied by Number of
default independent EEs
Collinear ∑ 𝑭𝒚 = 𝟎 1
∑ 𝑴𝒂𝒏𝒚 𝒑𝒐𝒊𝒏𝒕 𝒐𝒏 𝒙 = 𝟎
Concurrent at a ∑ 𝑴𝒐 = 𝟎 2
Point
Concurrent with a ∑ 𝑴𝒙 = 𝟎 5
Line
Parallel ∑ 𝑴𝒙 = 𝟎 3
∑ 𝑭𝒚 = ∑ 𝑭𝒛 = 𝟎
(b) (9 points) Draw the corresponding
Free Body Diagrams for the three
following cases
, 2
(a) (3 points) In the drawing to the right, the crate is kept in
equilibrium on an inclined rough surface as shown. What are
the two extreme cases and what is the direction of the friction
force in each of these cases (state and explain the cases, no
need to calculate).
Answer: The two extreme cases are (1) the block is about to slide down (friction is up the slope),
and (2) the block is about to be pushed up (friction is down the slope)
(b) (Bonus - 5 points) In each of the following
cases express the cable tension T in terms of
the weight of the crate.
Name
MECH 223 – Engineering Statics
Final Exam, May 4th 2015
Question 1 (20 + 5 points)
(a) (8 points) Complete the following table
Force System Free Body Diagram EEs satisfied by Number of
default independent EEs
Collinear ∑ 𝑭𝒚 = 𝟎 1
∑ 𝑴𝒂𝒏𝒚 𝒑𝒐𝒊𝒏𝒕 𝒐𝒏 𝒙 = 𝟎
Concurrent at a ∑ 𝑴𝒐 = 𝟎 2
Point
Concurrent with a ∑ 𝑴𝒙 = 𝟎 5
Line
Parallel ∑ 𝑴𝒙 = 𝟎 3
∑ 𝑭𝒚 = ∑ 𝑭𝒛 = 𝟎
(b) (9 points) Draw the corresponding
Free Body Diagrams for the three
following cases
, 2
(a) (3 points) In the drawing to the right, the crate is kept in
equilibrium on an inclined rough surface as shown. What are
the two extreme cases and what is the direction of the friction
force in each of these cases (state and explain the cases, no
need to calculate).
Answer: The two extreme cases are (1) the block is about to slide down (friction is up the slope),
and (2) the block is about to be pushed up (friction is down the slope)
(b) (Bonus - 5 points) In each of the following
cases express the cable tension T in terms of
the weight of the crate.
