Learning Goal: To practise Tactics Box 5.3 Working with ropes and pulleys. Objec

Question

Learning Goal: To practise Tactics Box 5.3 Working with ropes and pulleys. Objects are often connected by strings, ropes, cables, and so on. In many problems, the masses of the strings or ropes are significantly less than the masses of the objects they pull on. If, in addition, the strings or ropes pass over pulleys with negligible masses that turn almost freely on their axles, we can make two powerful simplifying working with ropes and pulleys For massless ropes or strings and massless, frictionless pulleys: If a force pulls on one end of a rope, the tension in the rope equals the magnitude of pulling force. If two objects are connected by a rope, the tension is the same at both ends. If the rope passes over a pulley, the tension in the rope is unaffected. Use these rules to solve this problem: A force F with magnitude F, is applied to rope 1 to fit block B and weight W with constant speed. (Figure 1) If the block's mass is m_B, what is the weight's mass m_w in terms of the known quantities F, m_B and g (the free-fall acceleration)? Assume that the ropes are massless, and that the pulleys are massless and frictionless. According to the first rule, if a force pulles on one end of a rope, the tension in the rope equals the magnitude of the pulling force. What is the magnitude T_1 of the tension in rope 1? Express your answer in terms od some or all of the variables F, m_B and g.

Explanation / Answer

here,

as the pulley is massless

the tension in the cable will be same throughout the cable

as the cable is also mass

hence, for the magnitude of tension T1

T1 = F

the tension in T1 is F

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