An Atwood's machine is built from m1=1kg and m2=2kg. The mass less string is passed over a friction less, mass less pulley. When the system is released from rest, what is the tension in the string?
force down:2*9.8
force up: 1*9.8
Net force= forcedown-forceup=ma
solve for a: mass=3kg
(9.8)(2-1)=3*a
a= 9.8/3
tension= mass*g-+mass*acceleration
tensionheavy side= 2(g-g/3)=4g/3
tensionlight side=1g+1g/3=4g/3
To find the tension in the string, we need to analyze the forces acting on each mass.
Let's consider m1 as the lighter mass and m2 as the heavier mass.
1. Determine the net force on m1:
- The only force acting on m1 is the tension in the string, pulling it upwards.
- The net force on m1 is given by Newton's second law: F1 = m1 * a1, where a1 is the acceleration of m1.
- Since the system is released from rest, the initial acceleration of both masses is zero.
2. Determine the net force on m2:
- The only force acting on m2 is the gravitational force pulling it downwards (m2 * g, where g is the acceleration due to gravity).
- The net force on m2 is given by Newton's second law: F2 = m2 * a2, where a2 is the acceleration of m2.
3. Relate the accelerations of m1 and m2:
- The two masses are connected by a massless string, so they experience the same magnitude of acceleration but in opposite directions.
- Thus, a1 = -a2.
4. Apply the tension force equation:
- The tension force in the string is the same for both masses.
- So, the magnitude of the tension force is given by: T = m1 * a1 = m2 * a2.
5. Solve for the tension in the string:
- Using the relation a1 = -a2, we can rewrite the equation: T = m1 * (-a2) = -m1 * a2
- Substituting the given masses: T = - 1 kg * a2
Now, we need to determine the acceleration of the system to find the tension in the string. For this, we can use the equation:
m1 * a1 - m2 * a2 = (m1 + m2) * g
Substituting the masses: 1 kg * 0 - 2 kg * a2 = (1 kg + 2 kg) * 9.8 m/s^2
-2 kg * a2 = 29.4 m/s^2
Solving for a2: a2 = -14.7 m/s^2
Finally, substitute the value of a2 into the equation for tension:
T = -1 kg * (-14.7 m/s^2) = 14.7 N
Therefore, the tension in the string is 14.7 Newtons.
To find the tension in the string of an Atwood's machine, you need to consider the masses involved and the direction of their motion. The tension in the string will vary depending on the difference in the masses between the two sides.
In an Atwood's machine, the masses on either side of the pulley are connected by a string, and the gravitational force acts on each mass.
In this case, m1 (mass 1) is 1kg and m2 (mass 2) is 2kg. The system is released from rest, which means both masses accelerate.
To find the tension in the string, we can use the following formula:
Tension (T) = (m2 - m1) * g
Where g is the acceleration due to gravity (approximately 9.8 m/s^2 on the Earth).
So, in this specific case, we have:
T = (2kg - 1kg) * 9.8 m/s^2
T = 1kg * 9.8 m/s^2
T = 9.8 Newtons
Therefore, the tension in the string of the Atwood's machine is 9.8 Newtons.