A mass of 2kg resting on a smooth level table is connected by a light in extensible string passing over a frictionless pulley to a suspended 3kg mass (imagine as shown on the diagram).Find:
I.The tension in the string.
II. The magnitude of the acceleration of the two masses.
III.The resultant force acting on the 3kg mass (g=10N kg^-1).
To find the answers to the given questions, we can use Newton's laws of motion and the concepts of forces, tension, and acceleration.
I. The tension in the string:
The tension in the string is the force that pulls the 2kg mass and the 3kg mass. Since the string is inextensible and connected over a frictionless pulley, the tension in the string is the same on both sides of the pulley.
1. Draw a free-body diagram for each mass to visualize the forces acting on them.
The 2kg mass has two forces acting on it: the weight force (mg) downwards and the tension force (T) upwards.
The 3kg mass also has two forces acting on it: the weight force (mg) downwards and the tension force (T) upwards.
2. Apply Newton's second law of motion to find the tension.
For the 2kg mass:
Sum of forces = mass × acceleration (since the mass is at rest, the acceleration is 0)
mg - T = 2kg × 0
mg = T
For the 3kg mass:
Sum of forces = mass × acceleration
mg - T = 3kg × acceleration
Since we need to find the tension, we can substitute the value of mg from the first equation into the second equation:
T = mg = 2kg × g = 2kg × 10N/kg = 20N
Therefore, the tension in the string is 20N.
II. The magnitude of the acceleration of the two masses:
Since the two masses are connected by the same string, they have the same acceleration.
Applying Newton's second law to the 3kg mass:
mg - T = 3kg × acceleration (from the first equation, T = mg)
3kg × g - 20N = 3kg × acceleration
Simplifying the equation:
30N - 20N = 3kg × acceleration
10N = 3kg × acceleration
Solving for acceleration:
acceleration = 10N / 3kg = 3.33 m/s²
Therefore, the magnitude of the acceleration of the two masses is 3.33 m/s².
III. The resultant force acting on the 3kg mass:
The resultant force can be calculated using Newton's second law:
Resultant force = mass × acceleration
resultant force = 3kg × 3.33 m/s² = 9.99N (approximately 10N)
Therefore, the resultant force acting on the 3kg mass is approximately 10N.