When two objects of unequal mass are hung vertically over a frictionless pulley of
negligible mass, as shown below, the arrangement is called an Atwood machine.
Determine a) the magnitude of the acceleration of the two objects and b) the tension in
the lightweight cord below form 2.00kg 1 = , and m 4.00kg 2 = .
can some one work this out for me i don't understand how to get the answers tothis problem
You need not the answers, but how to draw free body diagrams.
a. making the direction clockwise +, then
right weight -left weight=total mass*acceleration.
if acceleration is +, then it is moving clockwise. remember weight is mass*g
b. again, tension is easy. Pick a spot in the rope, I pick just above the right weight.
Tension-leftweight=leftmass*accelerationsolvedabove. How did I know that? Well, what is causeing the left mass to move? Ans: it is the amount of tension greater than massleft*g
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To find the magnitude of the acceleration and the tension in the lightweight cord of an Atwood machine, you can follow these steps:
1. Determine the net force: In an Atwood machine, the net force is given by the difference in the weights of the two masses. The weight of an object is given by the formula W = m * g, where m is the mass of the object, and g is the acceleration due to gravity (9.8 m/s^2).
For the first object (m1 = 2.00 kg), the weight is W1 = m1 * g.
For the second object (m2 = 4.00 kg), the weight is W2 = m2 * g.
2. Calculate the difference in weight: Subtract the weight of the lighter object from the weight of the heavier object to find the net force.
Net force (Fnet) = |W2 - W1|
3. Apply Newton's second law of motion: The net force (Fnet) is equal to the mass (m_total) of the system multiplied by the acceleration (a).
Fnet = m_total * a
Since the masses are connected and move together, the total mass (m_total) is given by the sum of the masses: m_total = m1 + m2.
4. Solve for acceleration: Rearrange the equation to solve for the acceleration (a).
a = Fnet / m_total
5. Calculate the tension in the lightweight cord: The tension in the cord can be found by considering the forces acting on each object. The tension in the cord below the first object is the force accelerating it, and the tension in the cord below the second object is the force decelerating it. Since the objects have the same acceleration in opposite directions, the tension in the cord below both objects is the same.
Tension (T) = m1 * g - m1 * a
Now, you can substitute the given values (m1 = 2.00 kg, m2 = 4.00 kg) and solve for the magnitude of acceleration (a) and the tension in the cord (T).
Note: The direction of acceleration will depend on which mass is larger. If m1 > m2, the lighter mass will accelerate upwards, and if m2 > m1, the lighter mass will accelerate downwards.