(a) What minimum force F is needed to lift the piano (mass M ) using the pulley
ID: 2276136 • Letter: #
Question
(a) What minimum force F is needed to lift the piano (mass M) using the pulley apparatus shown? (Enter your answers in terms of some multiple of Mg.)
Mg
(b) Determine the tension in each section of rope: FT1, FT2, FT3, and FT4.
Tension in FT1
Mg
Tension in FT2
Mg
Tension in FT3
Mg
Tension in FT4
Mg
Explanation / Answer
Dynamics - Net Force and Newton's Laws of Motion
Net force in this diagram is to the right.Net force is the unbalanced force acting on an object. When tow or more forces act on an object, the resultant (vector sum) of the forces is the net force. In the free body diagram on the left, the net force is to the right, so the object will accelerate to the right.
Most dynamics problems are based on one or a combination of Newton's Laws of Motion:
1. Newton's First Law of Motion (Law of Inertia): Every body continues in its state of rest or of uniform speed in a straight line unless it is compelled to change that state by a net force acting on it.
2. Newton's Second Law of Motion: The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the applied net force.
3. Newton's Third Law of Motion: Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first.
Examples
1.1 A 4kg object is moving across a frictionless surface with a constant velocity of 2 m/s. Determine the force necessary to maintain this state of motion
ANSWER TO EXAMPLE 1.1:
zero
Applying Newton's First Law of Motion, this object will continue its state of uniform speed in a straight line until a net (unbalanced) force acts upon it.
Applying Newton's Second Law of Motion, since acceleration is zero, the net force acting on the object is zero. An additional force applied to the object will cause an acceleration.
1.2 An object sits on a frictionless surface. There is a 16 N force being applied to an object and its acceleration is at 2 m/s/s. What is its mass?
ANSWER TO EXAMPLE 1.2:
Applying Newton's Second Law of Motion,
F = ma
16 N = m( 2 m/s2)
m = 8 kg
(related search terms: f=ma)
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