Question

1. A helicopter is lifting two crates simultaneously. Crate A, with a mass ma, is attached to the helicopter by a light cable (cable #1). Crate B, with a mass me, hangs below crate A and is attached to crate A by a second light cable (cable #2). The cables are NOT connected. The helicopter accelerates upward with an acceleration of magnitude a. Ignore all frictional effects. Let T be the tension in cable #1 and Tbe the tension in cable #2. a) WITHOUT PERFORMING ANY CALCULATIONS, decide which cable has a greater tension (cable #1, cable #2, neither)? WHY? b) Derive an expression for the tension in the lower cable T, in terms of the quantities given in the problem (ma, me and/or a) and, perhaps, constants (e.g., Tt, %, 9, ...). c) Derive an expression for the tension in the upper cable Ti in terms of the quantities given in the problem (ma, me and/or a) and, perhaps, constants (e.g., T, %, 9, ...). d) Evaluate numerical values for T, and T, if ma = 200 kg, ma-250 kg and the helicopter accelerates upward with an acceleration of magnitude 1.00 m/s. {T: 4.86 kN, T2 = 2.70 kN) d) If the helicopter moves vertically upward with constant velocity, which cable has a greater tension (cable #1, cable #2, neither)? WHY? Calculate the tensions in each cable. #1 НА #2 Св

Answer 1

a) cable #1 will experience more tension. As tension is only caused by the force acting on the cable and the force on #1 is of mass mA and mB both and on #2 it's only mB. And as mA and mB and non zero the tension in #1 is more than #2.

taking, mA= m1; mB=m2

c)Tension in #1:

Total mass acting on cable #1 ,M=m1+m2

Total acceleration acting on mass, A= a+g

Tension in #1,T1= MA= (a + g)(m1 + m2)

b)Tension in #2:

Similarly as #1

T2=(a+g)m2

d) m1=200kg, m2=250kg, a= 1m/s²

T1= (1 + 9.8).( 200+250)

= 10.8×450

T1=4860N=4.86kN

T2=10.8×250

=2700N=2.7kN

e) if the helicopter goes by constant speed , a=0

Therefore, T1= (g+0)×(m1×m2)

T1=( m1+m2)g

T2=gm2

As we can see, T1>T2