A light rope is attached to a block with a mass of 10 kg that rests on a horizontal, frictionless surface, and a block of mass, m, is suspended from the other end. The tension in the rope is 20 N when the blocks are released. a) What is the acceleration of the 10 kg block? b) What is the mass, m, of the hanging block?
To find the acceleration of the 10 kg block (a), you can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma).
In this case, the only force acting on the 10 kg block is the tension in the rope, so we can equate that to the mass (10 kg) multiplied by the acceleration (a). Therefore, the equation becomes:
Tension = mass * acceleration
Plugging in the given values, we have:
20 N = 10 kg * acceleration
Now, we can solve for acceleration:
acceleration = 20 N / 10 kg = 2 m/s^2
So, the acceleration of the 10 kg block is 2 m/s^2.
To find the mass (m) of the hanging block (b), we need to consider the forces acting on it. There are two forces: the tension in the rope pulling upward and the force due to gravity pulling downward.
The force due to gravity can be calculated using the equation:
Force due to gravity = mass * gravitational acceleration
Gravitational acceleration is approximately 9.8 m/s^2 on the surface of the Earth.
We know that the tension in the rope is 20 N, and this should be equal to the force due to gravity.
So, we can set up the equation:
20 N = m * 9.8 m/s^2
Now, we can solve for the mass (m) of the hanging block:
m = 20 N / 9.8 m/s^2
m ≈ 2.04 kg
Therefore, the mass (m) of the hanging block is approximately 2.04 kg.