Two blocks of mass 6 Kg and 4 kg kept on a rough surface are connected...
Given information:
- Mass of block 1 (m1) = 6 kg
- Mass of block 2 (m2) = 4 kg
- Coefficient of friction for both blocks (μ) = 0.5
- Force applied on block 1 (F) = 40 N
Solution:
First, we need to find the frictional force acting on each block.
Frictional force on block 1:
The frictional force on block 1 can be calculated using the formula:
Frictional force (f1) = μ * m1 * g
Where g is the acceleration due to gravity (9.8 m/s^2).
Substituting the given values:
f1 = 0.5 * 6 kg * 9.8 m/s^2 = 29.4 N
Frictional force on block 2:
The frictional force on block 2 can be calculated using the same formula:
Frictional force (f2) = μ * m2 * g
Substituting the given values:
f2 = 0.5 * 4 kg * 9.8 m/s^2 = 19.6 N
Net force on block 1:
The net force on block 1 can be calculated using the formula:
Net force (F1) = F - f1
Where F is the applied force on block 1.
Substituting the given values:
F1 = 40 N - 29.4 N = 10.6 N
Acceleration of the blocks:
The acceleration of the blocks can be calculated using the formula:
Acceleration (a) = net force / total mass
Where the total mass is the sum of the masses of the blocks.
Substituting the given values:
a = 10.6 N / (6 kg + 4 kg) = 1.06 m/s^2
Tension in the string:
The tension in the string can be calculated using the formula:
Tension (T) = m2 * a + f2
Substituting the given values:
T = 4 kg * 1.06 m/s^2 + 19.6 N = 23.84 N
Conclusion:
The tension in the string is 23.84 N.