A window washer of mass M is sitting on a platform suspended by mechanism of cables and pulleys as shown(Intro1 figure). He is pulling on the cable with a pressure of magnitude F. The cables and also pulleys are ideal (massless and also frictionless), and the platdevelop has actually negligible mass.
You are watching: Find the magnitude of the minimum force f that allows the window washer to move upward.
Find the magnitude of the minimum pressure F that permits the home window washer to move upward. Express your answer in regards to the mass M and also the magnitude of the acceleration due to gravity g.
The compelled concept to fix the given question is Newton’s second law of motion.
First, consider the forces acting on the device. Find an expression for the net force acting on the mechanism. Then take into consideration the condition for minimum pressure to be act on the system, use the problem in the expression of net pressure acting on the system. Rearrange and also simplify the above expression to attain the minimum pressure acting on the mechanism.
Force acting on a body may be characterized as the sudden press or pull which is capable of altering the direction of activity of the object if it is unopposed.
Newton’s second legislation says that “the acceleration of a things as produced by a net pressure is directly proportional to the magnitude of the used force and inversely proportional to the mass of the object”. It is in the exact same direction of the applied pressure.
The expression for pressure acting on an object is,
F=maF = maF=ma
Here, F is the force acting on the body, m is the mass of the object and also a is its acceleration.
Weight of an object is the “force of gravity”. It is characterized as the mass times the acceleration because of gravity.
Weight of the object is,
W=mgW = mgW=mg
Here, W is the weight of the object, m is the mass of the object and g is the acceleration due to gravity.
Regular force acting on the object is equal and oppowebsite to the gravitational force used on the object.
Net pressure acting on the system:
Here the perboy pulls the rope through a force F in the downward direction. The normal pressure N is acting alengthy the upward direction. It is equal to the pressure F.
Tension acting on the rope that supports the wheel,
T=2FT = 2FT=2F
Weight of the window washer W is acting downwards.
Net force acting on the mechanism,
Fnet=F+2F−W=3F−Mgeginarrayc\F_net = F + 2F - W\\ = 3F - Mg\endarrayFnet=F+2F−W=3F−Mg
Minimum force acting on the system:
For the minimum pressure, the net force acting on the mechanism is zero.
Minimum force acting on the device is,
Fnet=00=3Fmin−Mg3Fmin=MgFmin=Mg3eginarrayc\F_net = 0\\0 = 3F_min - Mg\\3F_min = Mg\\F_min = fracMg3\endarrayFnet=00=3Fmin−Mg3Fmin=MgFmin=3MgAns:
Magnitude of minimum force that enables that enables the window washer to move upward is Mg3fracfMgf33Mg.
This is a straightforward machine. Because the mass M is supported by not1, yet 2 strings, then the worker essentially has to pull through halfthe pressure to relocate itup. Conversely, if it were supported by 1string, he would should pull via pressure F.So we uncover that each string lessens the pressure he mustapply.F = .5mg <2 strings.>However, you should note that he would certainly should pull the cordtwice as far in order to move it the exact same distance as he would ifit were just supported by1 cord.So for 1 string, naturally pull:F = mg2 strings:F = .5mg3 strings:F =1/3mg4 strings:F = 1/4mg....and so on.
answered by: beena
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