Three identical blocks, A, B, and C, are on a horizontal frictionless table. The blocks are connected by strings of negligible mass, with block B between the other two blocks. If block C is pulled horizontally by a force of magnitude F = 28 N, find the tension in the string between blocks B and C.
m1=m2=m3 =m,
Total mass = 3 m.
Acceleration of each block
a= F/3•m.
T is the tension in the string between blocks B and C.
T is the pulling force on both masses B and A with an acceleration of a.
T = 2ma = 2•m• F/(3m) = 2/3•F = (2/3) •28 =18.7 N
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What is a term used to describe a system in which groups are ranked one above the other according to status?
taxonomy
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hierarchy
To find the tension in the string between blocks B and C, we need to analyze the forces acting on block C.
First, let's assume that the three blocks and the strings connecting them are all massless. This means that the force being applied to block C, F = 28 N, will be transmitted equally to blocks B and A through the strings.
Now, let's consider the forces acting on block C. We have the tension in the string between blocks B and C pulling block C to the right, and we have an equal tension in the string between blocks C and A pulling it to the left. Additionally, we have the applied force F pulling block C to the right.
Since the system is in equilibrium (no net acceleration), the sum of the forces in the horizontal direction must be zero.
Thus, we can set up the following equation:
Tension between B and C - Tension between C and A + Applied force F = 0
Since the forces in the strings are equal in magnitude (due to the assumption of massless strings), we can simplify the equation:
Tension between B and C - Tension between C and A + F = 0
Rearranging the equation, we can solve for the tension between B and C:
Tension between B and C = Tension between C and A - F
Since the tension in the string between C and A is the same as the tension in the string between B and C, we can substitute and simplify the equation further:
Tension between B and C = Tension between B and C - F
Now, let's solve for the tension between B and C:
2 * Tension between B and C = F
Tension between B and C = F / 2
Plugging in the force value F = 28 N, we get:
Tension between B and C = 28 N / 2
Tension between B and C = 14 N
Therefore, the tension in the string between blocks B and C is 14 N.