A 100kg mass is connected to a 200kg mass by a massless rope. The two masses rest on a frictionless surface. A (massless)rope is then attached to the 200kg mass, and is pulled. The two mass system accelerates. What is the relationship between the two tensions?
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The tension on the pulling rope is moving 300kg,the massless rope between the two is pulling 100kg. Sounds like tension is 3:1 ratio
Thanks, what a kick-mass answer!
To determine the relationship between the two tensions, we need to consider the forces acting on each mass separately.
Let's call the 100kg mass M1 and the 200kg mass M2. Since the entire system is on a frictionless surface, the only force acting on each mass is the tension in the rope attached to it.
For M1:
The tension in the rope connected to M1 pulls it towards the direction of acceleration. Let's call this tension T1.
For M2:
M2 is being pulled by two forces, one due to its own weight (mg, where g is acceleration due to gravity) and the other due to the tension in the rope connecting the two masses. Let's call this tension T2.
According to Newton's second law, the net force on an object is equal to its mass multiplied by its acceleration (F = ma). We can use this principle to set up equations for each mass.
For M1:
The tension T1 is the only force acting on M1, so we have:
T1 = M1 * a
For M2:
There are two forces acting on M2: its weight (mg) and the tension T2. The net force is equal to the product of mass and acceleration:
T2 - M2 * g = M2 * a
Now, to find the relationship between the two tensions, we can compare these equations.
From the first equation, we can express T1 in terms of M1:
T1 = M1 * a
From the second equation, we can express T2 in terms of M2 and the other variables:
T2 = M2 * (a + g)
Now, we can substitute these expressions for T1 and T2 into the second equation:
M1 * a = M2 * (a + g)
Now we can simplify and solve for the relationship between the two tensions:
M1 * a = M2 * a + M2 * g
M1 * a - M2 * a = M2 * g
(a * (M1 - M2)) / M2 = g
We can simplify further:
a / g = M2 / (M1 - M2)
From this equation, we can see that the relationship between the two tensions (T1 and T2) is determined by the masses M1 and M2, as well as the acceleration a and the acceleration due to gravity g.