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

where m1 = 6.21 kg and m2 = 19.5 kg. A force of 48.4 N

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

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

To find the answers to 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 times its acceleration.

1. To find the acceleration of the system, we can apply Newton's second law to the entire system of blocks. The only external force acting on the system is the applied force (48.4 N), and the mass of the system can be represented as the sum of the masses of the two blocks (m1 + m2). So, we have:

Net force = Applied force = (m1 + m2) * acceleration

Rearranging the equation, we can solve for acceleration:

acceleration = Applied force / (m1 + m2)

Substituting the given values:

acceleration = 48.4 N / (6.21 kg + 19.5 kg)

Calculating this, we find that the acceleration of the system is approximately 1.83 m/s^2.

2. To find the tension in the string between the blocks, we can consider the forces acting on each block individually. For block 1, there is tension force T acting to the right, and for block 2, there is tension force T acting to the left. Since the blocks are connected by a light string, the tension in the string is the same for both blocks.

Using Newton's second law for each block, we can write the following equations:

T - m1 * g = m1 * acceleration
m2 * g - T = m2 * acceleration

Simplifying these equations, we get:

T = m1 * (g + acceleration) = 6.21 kg * (9.8 m/s^2 + 1.83 m/s^2)

Calculating this, we find that the tension in the string between the blocks is approximately 85.963 N.

3. If there is friction on the surface, we need to consider the additional force due to friction. The frictional force can be calculated using the equation:

Frictional force = coefficient of kinetic friction * normal force

The normal force can be determined by calculating the weight of each block:

Normal force = m1 * g for block 1, and m2 * g for block 2

The coefficient of kinetic friction between the blocks and the surface is given as 0.1.

To find the new acceleration, we need to subtract the frictional force from the net force acting on the system. The net force can be calculated as the applied force minus the frictional force:

Net force = Applied force - Frictional force

Using Newton's second law, we can write:

Net force = (m1 + m2) * acceleration_new

Rearranging the equation, we can solve for acceleration_new:

acceleration_new = Net force / (m1 + m2)

Substituting the known values:

Net force = 48.4 N - frictional force

acceleration_new = (48.4 N - (coefficient of kinetic friction * (m1 * g + m2 * g))) / (m1 + m2)

Calculating this, we can find the new acceleration.

4. To find the new tension in the string between the blocks, we can use the same approach as in question 2. We need to consider the additional frictional force acting on each block.

Using Newton's second law for each block, we get:

T - m1 * g - Frictional force for block 1 = m1 * acceleration_new
m2 * g - T - Frictional force for block 2 = m2 * acceleration_new

By rearranging the equations and solving simultaneously, we can find the new tension in the string.

Step 1: Determine the net force on the system:

The force applied to the system is 48.4 N.
The mass of the system (m1 + m2) is 6.21 kg + 19.5 kg = 25.71 kg.

Using Newton's second law (F = ma), the net force on the system is equal to the mass of the system multiplied by the acceleration of the system:
48.4 N = 25.71 kg * a

Step 2: Solve for acceleration:
Divide both sides of the equation by the mass of the system:
a = 48.4 N / 25.71 kg

Calculating the value:
a ≈ 1.883 m/s^2

Therefore, the acceleration of the system is approximately 1.883 m/s^2.

Step 3: Calculate the tension in the string between the blocks:
Since the blocks are connected by a light string, the tension in the string is the same throughout the system.
Therefore, the tension in the string is equal to the force applied to the system:
Tension = 48.4 N

Therefore, the tension in the string between the blocks is 48.4 N.

Step 4: Calculate the new acceleration if there is friction:
The coefficient of kinetic friction between each block and the surface is 0.1.

The net force on the system is now the force applied minus the force of kinetic friction.

Force of friction (f) = coefficient of friction (μ) * normal force (N)

The normal force for each block is equal to the weight of the block (mass * acceleration due to gravity):
Normal force (N1) = m1 * g
Normal force (N2) = m2 * g

The force of friction for each block is:
Force of friction (f1) = μ * N1
Force of friction (f2) = μ * N2

Net force on the system:
Net force = Force applied (48.4 N) - Force of friction (f1) - Force of friction (f2)

Using Newton's second law (F = ma), the net force is equal to the mass of the system multiplied by the acceleration:
Net force = (m1 + m2) * a

Setting the two equations equal:
(m1 + m2) * a = Force applied - μ * N1 - μ * N2

Substituting the values:
(m1 + m2) * a = 48.4 N - 0.1 * (m1 * g) - 0.1 * (m2 * g)

Step 5: Solve for the new acceleration:
Divide both sides of the equation by (m1 + m2):
a = (48.4 N - 0.1 * (m1 * g) - 0.1 * (m2 * g)) / (m1 + m2)

Calculating the value:
a ≈ 1.838 m/s^2

Therefore, the new acceleration with friction is approximately 1.838 m/s^2.

Step 6: Calculate the new tension in the string between the blocks:
The tension in the string between the blocks is still equal to the force applied to the system:
Tension = 48.4 N

Therefore, the new tension in the string between the blocks with friction is 48.4 N.