1. Two blocks on a frictionless horizontal surface are connected by a light string.

The acceleration of gravity is 9.8 m/s^2. Find the acceleration of the system.
Answer in units of m/s^2.

2. What is the tension in the string between the blocks?
Answer in units of N.

3. If the surface were frictional, and the coefficient of kinetic friction between each block and the surface is 0.1, what would be the new
acceleration?
Answer in units of m/s^2.

4. What would be the new tension in the
string between the blocks?
Answer in units of N

What net force is acting on this system if both blocks are on the table?

6.21kg---19.5kg-----> 48.4 N

To answer your questions step-by-step:

1. To find the acceleration of the system, we need to analyze the forces acting on each block. Assuming the string and surface are massless, the tension in the string will be the same throughout. We can apply Newton's second law to each block separately:

For the first block (Block 1):
- Force acting vertically: Weight (m1 * g)
- Force acting horizontally: Tension in the string (T1)

Using Newton's second law:
m1 * a = T1 - m1 * g

For the second block (Block 2):
- Force acting vertically: Weight (m2 * g)
- Force acting horizontally: Tension in the string (T2)

Using Newton's second law:
m2 * a = T2 - m2 * g

Since the two blocks are connected and the string is light, the tension in the string is the same for both blocks (T1 = T2 = T). Therefore, we have:
m1 * a = T - m1 * g --(1)
m2 * a = T - m2 * g --(2)

Adding equations (1) and (2) together, we get:
m1 * a + m2 * a = T - m1 * g + T - m2 * g
(a * (m1 + m2)) = 2T - (m1 + m2) * g
a = ((2T - (m1 + m2) * g) / (m1 + m2))

2. To find the tension in the string between the blocks, we can substitute the value of acceleration (a) calculated above into one of the equations for the blocks. Let's use equation (1) for Block 1:
T1 = m1 * a + m1 * g

3. If the surface were frictional, with a coefficient of kinetic friction of 0.1 between each block and the surface, the forces acting on each block would include additional frictional forces.
For Block 1:
- Force due to friction: μk * (m1 * g), where μk is the coefficient of kinetic friction
- Force acting horizontally: Tension in the string (T1)

Applying Newton's second law:
m1 * a' = T1 - (μk * (m1 * g))

For Block 2:
- Force due to friction: μk * (m2 * g)
- Force acting horizontally: Tension in the string (T2)

Applying Newton's second law:
m2 * a' = T2 - (μk * (m2 * g))

Since the two blocks are connected and the tension in the string is the same for both blocks (T1 = T2 = T), we have:
m1 * a' = T - (μk * (m1 * g)) --(1)
m2 * a' = T - (μk * (m2 * g)) --(2)

Adding equations (1) and (2) together, we get:
m1 * a' + m2 * a' = 2T - μk * (m1 * g) - μk * (m2 * g)
a' * (m1 + m2) = 2T - (μk * (m1 + m2) * g)
a' = ((2T - (μk * (m1 + m2) * g)) / (m1 + m2))

4. To find the new tension in the string between the blocks with friction, we can substitute the value of acceleration (a') calculated above into one of the equations for the blocks. Let's use equation (1) for Block 1:
T1' = (m1 * a') + (μk * (m1 * g))

To solve the given problems, we need to understand the concept of Newton's second law of motion and apply it to the system of blocks connected by a string.

1. To find the acceleration of the system, we need to consider the forces acting on the blocks. Since there is no friction, the only force acting on the system is the force due to gravity. According to Newton's second law, the net force on an object is equal to its mass multiplied by its acceleration.

For this system, the net force acting on both blocks is the tension in the string. The tension is the same throughout the string since it is an inextensible string. Thus, we can write the equation as follows:

Tension = Mass1 * Acceleration
Tension = Mass2 * Acceleration

Since the masses are connected by the string, the tension is the force that accelerates both blocks. Therefore, the acceleration of the system is the same for both blocks.

Considering the equation: Tension = Mass * Acceleration, where Tension is the tension in the string and Mass is the total mass of the system, we can rearrange the equation to solve for the acceleration:

Acceleration = Tension / Mass

2. To find the tension in the string between the blocks, we need to consider the forces acting on each block. The force due to gravity acts on both blocks, and the tension in the string acts in the opposite direction for each block. Applying Newton's second law to each block, we have:

For Block 1:
Force gravity = Mass1 * Acceleration
For Block 2:
Force gravity = Mass2 * Acceleration

Since the tension in the string is the force that accelerates both blocks, we can set up the equation:

Tension - Force gravity = 0

Here, the force due to gravity is the weight of each block and can be calculated as:

Force gravity = Mass1 * gravity
Force gravity = Mass2 * gravity

Solving for the tension, we can substitute these equations into the tension equation:

Tension - (Mass1 * gravity) - (Mass2 * gravity) = 0

Simplifying this equation will give us the value of the tension.

3. If the surface were frictional, we need to consider the additional force acting on the blocks due to friction. The coefficient of kinetic friction determines the strength of this force. The force of kinetic friction is equal to the coefficient of kinetic friction multiplied by the normal force, where the normal force is the force exerted by the surface on the block.

The force of kinetic friction can be calculated using the equation:

Force kinetic friction = coefficient of kinetic friction * normal force

For each block, the normal force is equal to its weight:

Normal force = Mass1 * gravity
Normal force = Mass2 * gravity

To find the net force on each block, considering the force of kinetic friction, we can write the equation as follows:

For Block 1:
Net force1 = Tension - (Mass1 * gravity) - (coefficient of kinetic friction * Mass1 * gravity)
For Block 2:
Net force2 = Tension - (Mass2 * gravity) - (coefficient of kinetic friction * Mass2 * gravity)

Since the tension is the force that accelerates both blocks, the accelerations of both blocks will be the same. We can set the net forces equal to each other:

Net force1 = Net force2

Substituting the equations for the net forces, we can solve for the new acceleration:

Tension - (Mass1 * gravity) - (coefficient of kinetic friction * Mass1 * gravity) = Tension - (Mass2 * gravity) - (coefficient of kinetic friction * Mass2 * gravity)

Simplifying this equation will give us the value of the new acceleration.

4. To find the new tension in the string between the blocks when there is friction, we can use the same approach as in question 2. Once we have the new acceleration from question 3, we can set up the equation:

Tension - (Mass1 * gravity) - (coefficient of kinetic friction * Mass1 * gravity) = Tension - (Mass2 * gravity) - (coefficient of kinetic friction * Mass2 * gravity)

Simplifying this equation will give us the value of the new tension.