A 3.50 kg block on a smooth tabletop is attached by a string to a hanging block of mass 2.80 kg. The blocks are released from rest and allowed to move freely.

1-Is the tension in the string greater than, less than, or equal to the weight of the hanging mass?
2-Find the acceleration of the blocks.
3-Find the tension in the string.

1- Well, let me tell you a joke to answer your question. Why did the chicken go to the seance? To talk to the other side! Now, back to the question. In this case, the tension in the string is actually equal to the weight of the hanging mass. So, it's neither greater nor less than its weight. They literally balance each other out.

2- Now, let's calculate the acceleration. I just need to consult the speed of light... Just kidding! We can use Newton's second law of motion, which states that force equals mass times acceleration. Since there is a tension force acting on both blocks, we can write the equation as follows:

Tension force - Weight of the hanging mass = Total mass * Acceleration

Substituting the known values, the equation becomes:

T - (m2 * g) = (m1 + m2) * a

Where:
T is the tension force,
m1 is the mass of the block on the tabletop (3.50 kg),
m2 is the mass of the hanging block (2.80 kg),
g is the acceleration due to gravity (approximately 9.8 m/s^2),
and a is the acceleration we are trying to find.

Solving for a, we can find the acceleration of the blocks.

3- To find the tension in the string, we can use the equation we derived earlier:

T - (m2 * g) = (m1 + m2) * a

Solving this equation for T will give us the tension in the string. Voila!

1- The tension in the string is equal to the weight of the hanging mass.

2- To find the acceleration of the blocks, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. The net force can be determined by considering the forces on each block separately.

For the hanging mass:
The weight of the hanging mass can be calculated using the formula:
Weight = mass * gravitational acceleration = 2.80 kg * 9.8 m/s^2 = 27.44 N (rounded to two decimal places)

Since the hanging mass is in equilibrium, the tension in the string is equal to its weight, which is 27.44 N.

For the block on the tabletop:
The only force acting on the block is the tension in the string. According to Newton's second law, this tension force is equal to the mass of the block multiplied by its acceleration:
Tension = mass * acceleration
Tension = 3.50 kg * acceleration

Now, we can equate the tension force with the weight of the hanging mass:
Tension = Weight of Hanging Mass
3.50 kg * acceleration = 27.44 N

3- To find the tension in the string, we can divide both sides of the equation by 3.50 kg to isolate the acceleration:
acceleration = 27.44 N / 3.50 kg
acceleration ≈ 7.84 m/s^2 (rounded to two decimal places)

Therefore, the acceleration of the blocks is approximately 7.84 m/s^2.

To answer these questions, we can use Newton's second law of motion, which states that the net force on an object is equal to the mass of the object multiplied by its acceleration.

1- Is the tension in the string greater than, less than, or equal to the weight of the hanging mass?

The tension in the string will be equal to the weight of the hanging mass. The weight of an object is given by the mass multiplied by the acceleration due to gravity (9.8 m/s^2).

2- Find the acceleration of the blocks.

To find the acceleration, we need to consider the net force acting on the system. In this case, the only forces acting on the system are the weight of the hanging mass and the tension in the string.

The net force can be calculated as the difference between the weight of the hanging mass and the tension in the string:

Net force = Weight of hanging mass - Tension in the string

The weight of the hanging mass is equal to its mass multiplied by the acceleration due to gravity. So, it can be calculated as:

Weight of hanging mass = mass of hanging mass * acceleration due to gravity

Now, since the blocks are connected by a string, they will have the same acceleration. Therefore, the net force acting on both blocks will be the same. So, we can set up the following equation:

Net force = (mass of hanging mass + mass of block) * acceleration

Equating the two expressions for net force, we have:

Weight of hanging mass - Tension in string = (mass of hanging mass + mass of block) * acceleration

Simplifying the equation, we get:

Tension in string = (mass of hanging mass + mass of block) * acceleration - Weight of hanging mass

Now we can substitute the values given in the problem:
mass of hanging mass = 2.80 kg
mass of block = 3.50 kg
acceleration due to gravity = 9.8 m/s^2

Using the equation, we can solve for the acceleration.

3- Find the tension in the string.

Using the equation from question 2, we can solve for the tension in the string. Once we have the value of acceleration, we can substitute it into the equation along with the masses of the blocks and the weight of the hanging mass.

less than, the block is falling, so has to weigh less.

F=ma
2.80=(2.80+3.5)a solve for a

tension=2.80(g-a)