A light rope is attached to a block with a mass of 6 kg that rests on a horizontal, frictionless surface. THe horizontal rope passes over a frictionless, massless pulley, and a block of mass m is suspended from the other end. When the blocks are released, the tension in the rope is 18 N. a) what is the acceleration of the 6 kg block ? b) the mass m of the hanging block?
a) is 3 m/s
b) is 2.65 kg
I don't get the equations I should have used
Use Newton's second law:
F = m a
The tension of 18 N pulls on the 6 kg block, so it's acceleration is:
a = 18 N/(6 kg) = 3 m/s^2
Now the length of the rope can't change and it is pulled tight by the falling weight. This means that if the mass on the surface is accelerating at 3 m/s^2, the mass m is dropping downward with this acceleration.
The force on the hanging rope is (let's take the downward directon as positive):
F = m g - 18 N
But this has to equal m*a by Newton's second law and we know that a = 3 m/s^2.
m g - 18 N = m*(3 meters/s^2) --->
m = 18 N/[g - 3 m/s^2] = 2.64 kg
To solve for the acceleration of the 6 kg block, you can use Newton's second law, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, the tension in the rope is the force acting on the 6 kg block. So, you can set up the equation:
Tension = 18 N
Mass of the 6 kg block = 6 kg
Acceleration = ?
Using the equation F = ma, you can solve for acceleration:
18 N = 6 kg * acceleration
Dividing both sides of the equation by the mass (6 kg), you get:
acceleration = 18 N / 6 kg = 3 m/s^2
So, the acceleration of the 6 kg block is 3 m/s^2.
To find the mass (m) of the hanging block, you need to consider the forces acting on it. The force of gravity is pulling it downward, and the tension in the rope is pulling it upward.
The force of gravity acting on the hanging block is given by m*g, where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, the net force acting on the hanging block is:
Net force = m * g - tension
Using Newton's second law again, you can set up the equation:
m * g - 18 N = m * acceleration
Since the acceleration is already known (3 m/s^2), you can rearrange the equation to solve for m:
m = 18 N / (g - 3 m/s^2)
Substituting the value of g (approximately 9.8 m/s^2), you find:
m = 18 N / (9.8 m/s^2 - 3 m/s^2) ≈ 2.64 kg
So, the mass (m) of the hanging block is approximately 2.64 kg.