Block A of mass 2.0 kg and Block B of 8.0 kg are connected by a spring of spring constant 80 N/m and negligible mass. The system is being pulled to the right across a horizontal frictionless surface by a horizontal force of 4.0 N, with both blocks experiencing equal constant acceleration.

a) Calculate the force that the spring exerts on the 2.0 kg mass.
b) Calculate the extension of the spring.

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To calculate the force exerted by the spring on the 2.0 kg mass (Block A), we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement.

a) Calculate the force exerted by the spring on Block A:
- Step 1: Determine the displacement of the spring.
- Since both blocks are experiencing equal acceleration, they will have equal displacements.
- We can use Newton's Second Law to find the acceleration of the system:
- F = ma, where F represents the applied force and 'a' represents acceleration.
- Rearrange the equation to solve for acceleration: a = F/m.
- Plugging in the values, a = 4.0 N / (2.0 kg + 8.0 kg) = 0.4 m/s^2 (acceleration of the system).
- Since both blocks are accelerating, we can use the formula for displacement:
- d = (1/2) * a * t^2, where 'd' represents displacement, 'a' represents acceleration, and 't' represents time.
- In this case, t is not given, but we can leave it as 't^2' since we only need to find the relative displacement.
- Plugging in the values, d = (1/2) * 0.4 m/s^2 * t^2.
- Step 2: Apply Hooke's Law to calculate the force exerted by the spring.
- Hooke's Law states that the force exerted by a spring is given by F = kx, where 'F' represents the force, 'k' represents the spring constant, and 'x' represents the displacement.
- Rearrange the equation to solve for 'x': x = F/k.
- Plugging in the values, x = (k * d) / k = d.
- Therefore, the force exerted by the spring on the 2.0 kg mass is equal to the displacement, which we calculated as 'd'.

b) To calculate the extension of the spring:
- Since the spring exerts a force equal to the displacement (d) on Block A, we can use Hooke's Law to calculate the extension of the spring.
- Hooke's Law states that F = kx, where 'F' represents the force, 'k' represents the spring constant, and 'x' represents the extension or compression of the spring from its equilibrium position.
- Rearrange the equation to solve for 'x': x = F/k.
- Plugging in the values, x = d / k.
- Therefore, the extension of the spring is equal to the displacement (d) divided by the spring constant (k).