Find the tension of each rope.?

Question

Two blocks are fastened to the ceiling of an elevator. The elevator accelerates upward at 2.00 m/s2. The blocks both have a mass of 14.0 kg. Find the tension in each rope.

The blocks are arranged, rope 1 then block 1, then rope 2 starts at the bottom of block 1 then block 2 is at the bottom of rope 2.

Can someone show me how to do this, im not sure what equations to even use. Thanks

Answer 1

The most straight forward way to understand and solve these types of questions is to use free body diagrams of each mass and model the forces acting on the mass(versus the mass acting on something else). This will give you a set of simultaneous equations to solve for the variables of interest.

F=m*a
For static motion
sum(forces)=0
For accelerating motion
sum(forces)=m*a

Also set up a sign convention and use it when evaluating the free body diagrams

For both blocks the acceleration is 2 m/s upward
I will set upward as the positive direction

the sum of forces acting on block 1 are:
gravity, downward -m*g
tension in rope 1, T1 upward
tension in rope 2, T2, downward

summing and setting equal to m1*a


T1-T2-m1*g=m1*a
T1-T2=m1*(a+g)

Block 2

gravity downward
-m2*g
T2 upward

summing

T2-m2*g=m2*a

T2=m2(g+a)
you can solve for T2 since you know m2, g and a

T2=14*(9.81+2)
=165.34 N

Plugging into the first equation
T1-165.34=14*(9.81+2)
T1=330.68 N

j

Answer 2

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