Question

answer all parts of this free response question on your paper student answer document.
a construction crane is lifting a large, heavy air conditioner up to the top a tall building. the engineers are worried about the cable attached to the air conditioner breaking. the cable must support the air conditioner during three phases:

• phase a - when the motor is first turned on and the air conditioner is accelerating upwards
• phase b - when the air conditioner is moving upward at its highest constant velocity
• phase c - when the air conditioner is moving upward but slowing down to a stop

a. on the dot on your answer document draw a free - body diagram of the forces acting on the piece of equipment during phase b.
b. during which phase is the cable most likely to break?
a. during which phase is the cable most likely to break?
c. justify your choice in part b using evidence and reasoning.
answer this question on paper.

Explanation:

Step1: Analyze forces in each phase using Newton's second law \(F = ma\)

• Phase A: The air - conditioner is accelerating upwards. Let the mass of the air - conditioner be \(m\), the acceleration due to gravity be \(g\), and the acceleration of the air - conditioner be \(a\). According to Newton's second law \(F_{net}=T - mg=ma\), where \(T\) is the tension in the cable. So, \(T = m(g + a)\).
• Phase B: The air - conditioner is moving at a constant velocity. Using Newton's second law \(F_{net}=T - mg=0\) (since \(a = 0\) for constant velocity). So, \(T=mg\).
• Phase C: The air - conditioner is decelerating (slowing down) while moving upwards. Let the deceleration be \(a'\). According to Newton's second law \(F_{net}=mg - T=ma'\), so \(T=m(g - a')\).

Step2: Compare the tension values

Since \(m(g + a)>mg>m(g - a')\), the tension in the cable is maximum in Phase A. And the cable is most likely to break when the tension \(T\) in it is maximum.

for Part A (Free - body diagram for Phase B):

• Forces acting on the air - conditioner:
• Gravitational force (\(F_g\)): Acts downwards and is given by \(F_g = mg\), where \(m\) is the mass of the air - conditioner and \(g\) is the acceleration due to gravity.
• Tension in the cable (\(T\)): Acts upwards.
• Since the air - conditioner is moving at a constant velocity in Phase B, according to Newton's first law (a special case of Newton's second law where \(a = 0\)), the net force \(F_{net}=T - F_g=0\). So, the free - body diagram will have two equal and opposite forces: \(T\) (upwards) and \(F_g\) (downwards).

Answer:

a. Phase A