To find the velocity of the two blocks when block A has moved 3m, we can use the work-energy principle.
To start, let's define the variables:
m1 = mass of block A (16kg)
m2 = mass of block B (8kg)
μ = coefficient of kinetic friction (0.4)
F = force acting on block A (200N)
d = distance block A has moved (3m)
v1 = velocity of block A
v2 = velocity of block B
Now, let's break down the problem into steps to find the solution:
Step 1: Calculate the work done on block A:
The work done on block A is given by the equation: W = F * d * cosθ
Since the force is acting towards the center of the table surface, the angle between the force and the displacement is 0 degrees. Therefore, cosθ = 1.
So, the work done on block A is: W = 200N * 3m * 1 = 600J
Step 2: Calculate the work done against friction:
The work done against friction is given by the equation: W = μ * m1 * g * d
Using the given values, we can calculate the work done against friction:
W = (0.4) * (16kg) * (9.8m/s^2) * (3m) = 188.16J
Step 3: Calculate the change in kinetic energy:
The change in kinetic energy is given by the equation: ΔK = K2 - K1
Since the system starts from rest, the initial kinetic energy of both blocks is zero, so K1 = 0.
Therefore, ΔK = K2 - 0 = K2
Step 4: Apply the work-energy principle:
According to the work-energy principle, the work done on a system is equal to the change in kinetic energy of the system.
So, W = ΔK
Rearranging the equation, we get:
600J - 188.16J = K2
K2 = 411.84J
Step 5: Calculate the final velocity of block A:
The final velocity of block A can be calculated using the equation: K2 = (1/2) * m1 * v1^2
Rearranging the equation, we get:
v1 = √(2 * K2) / m1
v1 = √(2 * 411.84J) / 16kg
v1 ≈ 4.04 m/s
Step 6: Calculate the final velocity of block B:
Since block A and block B are connected by a light rope, they have the same velocity.
Therefore, v2 = v1 ≈ 4.04 m/s
Thus, the velocity of the two blocks when block A has moved 3m is approximately 4.04 m/s.