Problem Set 1
Problem 1 (5 points) : A sailing ship can be modeled as shown in Fig 1. In Fig 1, the
forward sail is modeled as a 45-45-90 right triangle and the rear sail is a 30-60-90 right
triangle. Each sail experiences a tangential force of 1.0X102 N. What is the total forward
force acting on the ship?
Fig 1: A sailing ship (left) and a simplified drawing for analysis.
Solution:
Problem Set 1
Problem 2 (10 points): A ship is tied to the pier as shown in Fig 2. Points A and B are 6.0
m above (in the z direction) points C and D. The tension in line CA is 2.0 kN. The tension
in line BD is 3.0 kN. All distances shown are in meters. What is the net force acting on the
vessel? Convey your answer using i,j,k notation.
Y
Z
A
A
Vessel
B
X
1.0 x 101 m
C
D
C
6.0 m
PIER
2.0 m
Fig 2: Overhead view of a ship tied to a pier. Note: the photo on the left is not an overhead view.
Solution:
Problem Set 1
Problem 3 (10 points): A group of intrepid campers decides to pull down a tree (it was
already leaning). They need to ensure that the force parallel to tree AB is less than or
equal to 500 N (to prevent the wood from compressing*). The campers attach a rope to
point B, and stand at point C, as shown on Fig 3. Point B is (-1,1,10) and point C is
(20,20,0). All distances are in meters. What is the maximum force that can be applied to
the rope?
Z
B
A
Y
C
X
Fig 3: Diagram of rope being
used to pull a tree down.
* Note: These campers are not helluva engineers,
their concern over compressing wood with the force
they can apply with their rope is not well informed.
Solution: