a 5 kg object placed on a frictionless,horizontal table is connected to a string that passes over a pulley and then is fastened to a hanging 9kg objct.find the acceleration of the two objcts and the tension in the string
pulling force=totalmass*acceleration
9g=(9+5)a
To find the acceleration of the two objects and the tension in the string, we need to use Newton's second law and consider the forces acting on each object.
Let's denote the mass of the 5 kg object as m1 and the mass of the 9 kg object as m2. The tension in the string can be denoted as T.
First, let's consider the 5 kg object on the frictionless table. The only force acting on it is the tension in the string (T). According to Newton's second law, the net force (F1) acting on the object is equal to the mass (m1) multiplied by the acceleration (a):
F1 = m1 * a
Next, let's consider the 9 kg hanging object. The force of gravity (weight) acts downward, and the tension in the string (T) acts upward. The net force (F2) acting on the object is equal to the difference between the weight and the tension:
F2 = m2 * g - T
Since the two objects are connected by the string and pulley system, they have the same acceleration (a). This can be stated as:
a = a1 = a2
Now, we can solve the system of equations to find the values of acceleration (a) and tension in the string (T).
1. Substitute the value for F1 into the first equation:
m1 * a = F1
2. Substitute the value for F2 into the second equation:
m2 * g - T = F2
3. Since a1 = a2, substitute a into the equations:
m1 * a = m2 * a
4. Rearrange the equation to solve for the tension (T):
m2 * g - T = m1 * a
5. Substitute the value for a from the second equation into the fourth equation.
6. Rearrange the equation to solve for the acceleration (a):
a = m2 * g / (m1 + m2)
7. Substitute the value of a back into the fourth equation to find the tension (T).
Using these steps, you can plug in the given values for m1, m2, and g (acceleration due to gravity) to find the acceleration and tension in the string.