a block of mass 5.62 kg lies on a frictionless horizontal surface. The block is connected by a cord passing over a pulley to another block of mass 2.53 kg which hangs in the air. Calculate the Acceleration of the first block. The acceleration of gravity is 9.8 m/s square root of 2. Amswer in units of m/s square root of 2.
To calculate the acceleration of the first block, we need to consider the forces acting on it.
1. The weight of the first block (m1*g): Since the surface is frictionless, this force does not affect the horizontal motion.
2. The tension force from the hanging block (m2*g): This force acts horizontally to the right.
3. The net force: Since the net force causes acceleration, we need to determine the net force acting on the first block.
Using Newton's second law of motion (F = m*a) and considering the forces mentioned above, we can write the equation:
m1 * a = m2 * g - T
where:
m1 = mass of the first block = 5.62 kg
m2 = mass of the second block = 2.53 kg
g = acceleration due to gravity = 9.8 m/s^2
T = tension force, which can be determined using the hanging mass:
T = m2 * g
Substituting the values into the equation:
5.62 * a = 2.53 * 9.8 - (2.53 * 9.8)
5.62 * a = 24.6864 - 24.6864
5.62 * a = 0
a = 0 m/s^2
Therefore, the acceleration of the first block is 0 m/s^2.
To calculate the acceleration of the first block, we need to consider the forces acting on it.
1. Tension force (T): The tension force in the cord will be the same for both blocks since they are connected by the same cord.
2. Weight (W1): The weight of the first block equals its mass (m1) multiplied by the acceleration due to gravity (g).
3. Net force: The net force acting on the first block is the difference between the tension force and the weight.
Now let's calculate the acceleration using Newton's second law:
Net force = m1 * a
The net force is given by:
T - W1 = m1 * a
The equation for weight is:
W1 = m1 * g
Therefore, we can rewrite the equation as:
T - m1 * g = m1 * a
Since the tension force (T) is the same as the weight of the second block (m2 * g), we can substitute that into the equation:
m2 * g - m1 * g = m1 * a
Now let's plug in the given values:
m1 = 5.62 kg
m2 = 2.53 kg
g = 9.8 m/s^2
Substituting these values, we have:
(2.53 kg * 9.8 m/s^2) - (5.62 kg * 9.8 m/s^2) = (5.62 kg) * a
Simplifying further:
24.7844N - 55.076 kg·m/s^2 = 5.62 kg · a
Now we can solve for acceleration (a):
a = (24.7844N - 55.076 kg·m/s^2) / 5.62 kg
Calculating the acceleration with these values:
a ≈ -5.86 m/s^2
Since the question asks for the answer in units of m/s√2, we can convert the acceleration:
a ≈ -5.86 m/s^2 * (√2 m/s) / (√2 m/s) ≈ -5.86√2 m/s^2
Therefore, the acceleration of the first block is approximately -5.86√2 m/s^2.