Statics
Forces in equilibrium
§ 5.1
What’s the point?
• How do forces balance?
• What forces must structures withstand?
• What is the result of non-balancing forces?
Poll Question
weight
1m
T
8m
T
A hammock slung between trees 8 m apart sags
1 m when a person lies in it. The tension in each
rope holding the hammock is
A.
B.
C.
D.
Equal to the weight of the person.
Half the weight of the person.
More than the weight of the person.
Less than the weight of the person, but more than half.
Whiteboard Problem
weight
1m
T
T
8m
• Identify the forces acting on the hammock.
• Draw a free-body diagram for the
hammock.
• Find the components of all the forces.
Free-body Diagram
tension
tension
weight
Acceleration = 0, so forces add to zero
Observe the magnitudes!
So, for the hammock…
• Tension is the same direction as rope
stretch: 4 horizontal: 1 vertical
• Add up the vectors!
4
1
2
1
Here,
tension is
over twice
the weight!
Dynamics
acceleration
§ 5.2
Example Problem 4.1001
A person pulls on a rope attached to an initially
motionless 25-kg box on a frictionless plane
inclined 30° to the horizontal. She pulls with a
force of 20 N parallel to the plane of the ramp.
Find the speed and position of the box after 5 s.
30°
Example Problem
A cart of mass M is attached to a free-hanging
weight of mass m over a frictionless pulley by a
massless string. Find the acceleration of the cart
and the tension in the rope.
M
m