An object of mass m1 hangs from a string that passes over a very light fixed pulley P1 as shown in Figure P4.68. The string connects to a second very light pulley P2. A second string passes around this pulley with one end attached to a wall and the other to an object of mass m2 on a frictionless, horizontal table, (a) If a1 and a2, are the accelerations of m1 and m2, respectively, what is the relation between these accelerations? Find expressions for (b) the tensions in the strings and (c) the accelerations a1 and a2? in terms of the masses m1 and m2. and g.
Figure P4.68
(a)
Answer to Problem 68AP
Introduction:
The acceleration produces on the masses or bodies due to the application of external forces on it. In the presence of external force the acceleration produced in the same direction as that of the force.
Explanation of Solution
Here the two masses are affected by tensions and those are the reasons for the acceleration of the two masses
The tensions those are affected on the strings are same. Thus the acceleration on the mass
Conclusion:
Therefore, the acceleration on mass
(b)
Answer to Problem 68AP
Solution:
The magnitude of tensions are
Explanation of Solution
Given Info:
The acceleration of mass
Write the expressions for tensions on two strings attached by two masses.
Write (I) in terms of
Write the relation between the two accelerations.
Rewrite the equation (III) using (IV).
Rewrite (II) in terms of
Write the expression for tension in pulley 2.
Rewrite the above expression in terms of
Substitute (VI) and (VII) in (V) to calculate
Substitute (VIII) in (VII) to calculate
Conclusion:
Therefore, the magnitude of tensions are
(c)
Answer to Problem 68AP
Solution:
The magnitude of accelerations
Explanation of Solution
Given Info:
Write the formula to calculate
Use
Substitute the above expression in (IV) to calculate
Conclusion:
Therefore, the magnitude of accelerations
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Chapter 4 Solutions
College Physics
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