In the scenario depicted below, all surfaces are frictionless. The masses are gi
ID: 1622923 • Letter: I
Question
In the scenario depicted below, all surfaces are frictionless. The masses are given as M_1, M_2, M_3 as on the diagram. Mass M_1 is free to slide on a surface at rest relative to the surface of the Earth (like a smooth table). Let the positive x-direction point to the right, and let the positive y-direction point upward. Analyze this system from a reference frame at rest relative to the surface on which block 1 is free to slide this is an inertial frame. a. For each of the objects1.2, 3, name any other objects that are exerting a force on it. For each of these forces, if the direction of the force is known, assign a variable to the magnitude of this force. If the direction of the force is unknown, assign a variable to nonzero the component (s) of this force. b. Write down an expression for the sum of the forces on each object. c. Write down Newton's Second Law for each object, and count the number of equations and unknowns you have d. Determine an equation relating the accelerations of blocks 1 and 3 in the x-direction. e. Nothing this hard will be on the exam. Try to find another independent equation relating various components of the accelerations of the three blocks. f. Optional/difficult! Solve for the acceleration of block 1 in terms of the masses and g. Check the units of your expression, and try to determine if there are any limiting cases you can check as well.Explanation / Answer
Solution:
a) The forces acting on the block M2 is the Tension force T directed towards the pulley .
For M3 the tension T along the rope connecting M2 and M3 is directed upwards towards the pulley ,
The second force acting on M2 is its weight , the gravity force M2g acting vertically downwards. For M1 , M1g is the gravity force which acts on it .
b) For the mass M 2 , T - M2g = M2a
and M3g - T =M3a
c) The above equations are the Newton's 2nd law of the equations for the two masses .
d) Along the X direction , M2 ahs the mass .
Along X direction , M3 has no acceleration . M3 has its acceleration in the vertical direction .
acceleration for the mass M2 is a = (M3 - M2 ) g / (M2 + M3)