Q.17: In the Figure 3.22 find the acceleration of the masses and the tension in the string.
We do not see figure 3.22. If you make a description of the figure, we might be able to help you.
o.98m/s2 and 223.11N
To find the acceleration of the masses and the tension in the string in Figure 3.22, we need more information. Could you please provide a detailed description or a diagram of the figure?
To find the acceleration of the masses and the tension in the string, we need to analyze the forces acting on each mass and apply Newton's second law of motion.
First, let's consider the forces acting on each mass:
1. Mass m1 (on the left):
- The force of gravity acts downwards, equal to m1 * g, where g is the acceleration due to gravity.
- The tension T in the string acts towards the right.
2. Mass m2 (on the right):
- The force of gravity acts downwards, equal to m2 * g.
- The tension T in the string acts towards the left.
Next, we can apply Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
For mass m1:
- Net force = T - m1 * g
- Mass m1 * acceleration = T - m1 * g
For mass m2:
- Net force = m2 * g - T
- Mass m2 * acceleration = m2 * g - T
Since the masses are connected by a string, their accelerations will be the same. Let's call it 'a' (acceleration).
Now, we have two equations:
1. m1 * a = T - m1 * g ----(Equation 1)
2. m2 * a = m2 * g - T ----(Equation 2)
To solve for 'a' and 'T', we have two unknowns and two equations. We can use these equations to find the values of 'a' and 'T'.
First, let's rearrange equation 1 to solve for 'T':
T = m1 * a + m1 * g
Now, substitute this value of 'T' into equation 2:
m2 * a = m2 * g - (m1 * a + m1 * g)
m2 * a = m2 * g - m1 * a - m1 * g
(m1 + m2) * a = (m2 - m1) * g
a = ((m2 - m1) * g) / (m1 + m2)
Once we have the value of 'a', we can substitute it into equation 1 to find the tension 'T':
T = m1 * a + m1 * g
Now you can plug in the values for m1, m2, and g from Figure 3.22 to calculate the acceleration 'a' and the tension 'T' in the string.