Suppose a cord is a heavy rope of mass 1.0 kg. Calculate the acceleration of each box and the tension at each end of the cord, using the free-body diagrams. Assume the cord doesn't sag. (m1 = 8.5 kg , m2 = 12.5 kg and FP = 36.0 N)
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To calculate the acceleration of each box and the tension at each end of the cord, let's break down the problem step by step using free-body diagrams.
Step 1: Draw the free-body diagram for the first box (m1):
- On m1, there are two forces acting: its weight (m1*g) downwards and the tension force (T1) upwards.
- Since m1 is not accelerating vertically, the net force on m1 in the vertical direction is zero.
- This leads to the equation: T1 - m1*g = 0, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
- Rearranging the equation, we get T1 = m1*g.
Step 2: Draw the free-body diagram for the second box (m2):
- On m2, there are three forces acting: its weight (m2*g) downwards, the tension force (T2) upwards, and the applied force (FP) to the right.
- In the vertical direction, the net force on m2 is zero, as it is not accelerating vertically. This gives us: T2 - m2*g = 0.
- In the horizontal direction, the net force on m2 is given by: FP - T2 = m2*a, where a is the acceleration of m2.
- Using the value of T2 from the equation above, we can rewrite this equation as: FP - m2*g = (m2*a).
Step 3: Solve the equations simultaneously:
- We have two unknowns: T1 and T2, and two equations from the free-body diagrams.
- Substitute the known values for m1, m2, g, and FP into the equations.
- Solve the equations simultaneously to find the values of T1 and T2.
- Once you have obtained the values of T1 and T2, you can calculate the acceleration (a) using the second equation from Step 2.
Note: Ensure consistent units are used throughout the calculations. If necessary, convert units to a common system (e.g., SI units) before performing calculations.
Remember, always double-check your work and equations to ensure accuracy.