Three blocks of mass 1kg,2kg and 3kg move on a frictionless surface and a horizontal force 46 N acts on the 3kg block.1kg and 2kg blocks are in contact with each other while 1kg and 3kg blocks are connected by a chord.

(a) Determine the acceleration of the system
(b) Determine the tension in the cord connecting the 3.0 kg and the 1.0 kg blocks.

(c) Determine the magnitude of the force exerted by the 1.0 kg block on the 2.0 kg block.

a) The applied force of F = 46N acts on the system of all three blocks. You can ignore the internal foces (cord and contact) between blocks and apply F = (M1 + M2 + M3) a, where M1 = 1 kg, M2 = 2 kg and M3 = 3 kg.

a = 46 N/6 kg = 23/3 m/s^2

b) Let f1 be the cord tension. Only F and f1 act on M3, the 3 kg mass. Apply Newton's law.
F - f1 = M3 * a
Solve for f1. Use the value of a from part (a)
(c) The only force applied to M2 is the contact force from M1. Call it f2. Solve
f2 = M2 a

Thanks a lot for your timely help.

To solve this problem, we will use Newton's second law, which states that the net force applied to an object is equal to the product of its mass and acceleration (F = ma).

(a) Determine the acceleration of the system:
To find the acceleration of the system, we need to calculate the net force acting on the blocks. Since the surface is frictionless, the only horizontal force acting on the blocks is the applied force of 46 N on the 3 kg block.

First, let's find the net force on the 3 kg block:
F_net = F_applied - Tension
F_net = 46 N - Tension

Next, let's find the net force on the 2 kg block:
The 2 kg block is in contact with the 1 kg block, so it experiences the same acceleration as the 1 kg block. Therefore, the force exerted on the 2 kg block by the 1 kg block is equal to the force exerted on the 1 kg block:

Force exerted by the 1 kg block on the 2 kg block = F_net = 46 N - Tension

Now, let's find the acceleration of the system using the net force on the 3 kg block:
F_net = ma
46 N - Tension = (3 kg)(a)

Next, let's consider the forces acting on the 1 kg block:
The 1 kg block is connected to the 3 kg block by a cord, so it experiences the same acceleration (a) as the 3 kg block. The force exerted by the cord on the 1 kg block is equal to the tension (Tension). Since there are no other horizontal forces acting on the 1 kg block, the net force on the 1 kg block is also equal to the tension (Tension).

Force exerted by the cord on the 1 kg block = Tension

Using Newton's second law for the 1 kg block:
Tension = (1 kg)(a)

Since both the 3 kg and 1 kg blocks have the same acceleration (a), we can set their expressions for tension equal to each other:

46 N - Tension = Tension
46 N = 2Tension

Solving for Tension:
Tension = 46 N / 2
Tension = 23 N

Now, let's substitute Tension into the equation for F_net to find the acceleration:
46 N - Tension = (3 kg)(a)
46 N - 23 N = (3 kg)(a)
23 N = (3 kg)(a)
a = 23 N / 3 kg
a = 7.67 m/s^2

Therefore, the acceleration of the system is 7.67 m/s^2.

(b) Determine the tension in the cord connecting the 3.0 kg and the 1.0 kg blocks:
We have already calculated the tension in part (a).
Tension = 23 N

Therefore, the tension in the cord connecting the 3.0 kg and the 1.0 kg blocks is 23 N.

(c) Determine the magnitude of the force exerted by the 1.0 kg block on the 2.0 kg block:
The force exerted by the 1 kg block on the 2 kg block is equal to the force exerted on the 1 kg block, which is the tension.

Force exerted by the 1.0 kg block on the 2.0 kg block = Tension = 23 N

Therefore, the magnitude of the force exerted by the 1.0 kg block on the 2.0 kg block is 23 N.

To determine the acceleration of the system, we will use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

(a) Determine the acceleration of the system:
First, we need to figure out the net force acting on the system. Since the only force acting on the system is the horizontal force of 46 N applied to the 3 kg block, the net force will be 46 N.

Next, we can calculate the total mass of the system by adding the masses of the three blocks, which gives us 1 kg + 2 kg + 3 kg = 6 kg.

Now we can apply Newton's second law to find the acceleration of the system:
Net Force = mass * acceleration
46 N = 6 kg * acceleration

To solve for the acceleration, divide both sides of the equation by 6 kg:
acceleration = 46 N / 6 kg
acceleration ≈ 7.67 m/s^2

(b) Determine the tension in the cord connecting the 3.0 kg and the 1.0 kg blocks:
The tension in the cord connecting the 3 kg and 1 kg blocks is the same because they are in contact and experiencing the same acceleration.

We can find the tension by isolating the 3 kg block and applying Newton's second law to it. The only force acting on the 3 kg block is the tension in the cord, which is pulling it to the right. The mass of the 3 kg block is 3 kg, and we already know the acceleration of the system from part (a), which is 7.67 m/s^2.

Tension = mass * acceleration
Tension = 3 kg * 7.67 m/s^2
Tension ≈ 23.01 N

Therefore, the tension in the cord connecting the 3.0 kg and the 1.0 kg blocks is approximately 23.01 N.

(c) Determine the magnitude of the force exerted by the 1.0 kg block on the 2.0 kg block:
Since the 1 kg and 2 kg blocks are in contact, they also experience the same acceleration. To find the force exerted by the 1 kg block on the 2 kg block, we need to consider the forces acting on the 2 kg block.

The only forces acting on the 2 kg block are the force exerted by the 1 kg block and the force of gravity acting vertically downwards. We can assume that there is no vertical acceleration, so the net force in the vertical direction is zero.

The force exerted by the 1 kg block on the 2 kg block is equal in magnitude and opposite in direction to the force exerted by the 2 kg block on the 1 kg block.

Therefore, the magnitude of the force exerted by the 1.0 kg block on the 2.0 kg block is the same as the magnitude of the force exerted by the 2.0 kg block on the 1.0 kg block, which is equal to the tension in the cord.

So, the magnitude of the force exerted by the 1.0 kg block on the 2.0 kg block is approximately 23.01 N.