A block of mass 3kg which is on a smooth inclined plane making an angle of 30° to the horizontal is connected by a cord passing over a light frictionless pulley to a second block of mass 2kg hanging vertically. What is the acceleration of each block and what is the tention of thr cord?
Stupid answer it's wrong
The 2 kg hanging block:
x defined down
m a = m g - T
T = m (g-a)
T = 2 (9.81-a)
The 3 kg bock on the slope:
now x is up the slope
T - m g sin 30 = m a
T = m (g/2+a)
T = 3 (4.9-a)
your turn.
m1gsin30=3×9.8×1/2=14.7 (take g=9.8)
m2g=2×9.8=19.6
14.7-T=3a --------(1)
T-19.6=2a ---------(2)
By solving 1 and 2 we get a=-4.9
(-) indicates direction
a=4.9
By substituting a=4.9 in any equation,we get T=17.6N
a=0.98m/s2
stupid donkey wrong answer
To find the acceleration of each block and the tension in the cord, we can apply Newton's second law of motion to both blocks separately.
Let's start by analyzing the forces acting on the 3kg block on the inclined plane:
1. Gravitational force (mg): The weight of the block acts straight downward. Since the block is on an inclined plane, we need to resolve this force into two components:
- The component parallel to the plane is mg * sin(30°).
- The component perpendicular to the plane is mg * cos(30°).
2. Normal force (N): This force acts perpendicular to the plane. It counteracts the component of the gravitational force acting perpendicular to the plane. So, N = mg * cos(30°).
3. Friction force (f): Since the inclined plane is smooth (assumed to have no friction), there is no friction force acting on the block.
Now, let's analyze the forces acting on the 2kg hanging block:
1. Gravitational force (mg): This force acts straight downward.
2. Tension in the cord (T): This force acts upward and is responsible for accelerating the block.
Applying Newton's second law to each block:
For the 3kg block:
Sum of forces = Mass * Acceleration
Taking the direction along the incline as the positive direction, we have:
mg * sin(30°) - T = 3kg * acceleration (equation 1)
For the 2kg hanging block:
Sum of forces = Mass * Acceleration
mg - T = 2kg * acceleration (equation 2)
To solve these equations simultaneously, we need to eliminate the tension (T) by adding equation 1 and equation 2:
mg * sin(30°) + mg - T + T = 3kg * acceleration + 2kg * acceleration
Simplifying the equation:
mg * sin(30°) + mg = 5kg * acceleration
Now, we can substitute the value of g and simplify further:
(9.8 m/s^2) * (1/2) + (9.8 m/s^2) = 5kg * acceleration
4.9 m/s^2 + 9.8 m/s^2 = 5kg * acceleration
Acceleration = (4.9 m/s^2 + 9.8 m/s^2) / 5kg
Acceleration = 14.7 m/s^2 / 5kg
Acceleration ≈ 2.94 m/s^2
Now, to find the tension in the cord, we can substitute the acceleration value back into either equation 1 or equation 2:
Using equation 1:
mg * sin(30°) - T = 3kg * acceleration
(3kg) * (9.8 m/s^2) * (1/2) - T = (3kg) * (2.94 m/s^2)
14.7 N - T = 8.82 N
T = 14.7 N - 8.82 N
T ≈ 5.88 N
Therefore, the acceleration of each block is approximately 2.94 m/s^2, and the tension in the cord is approximately 5.88 N.