When a horizontal force of 7N acts on a block on a resistance free surface, it produces an acceleration of 3.5m/s^2. suppose a second 4kg block is dropped onto the first. what is the magnitude of the acceleration of the combination if the same force continues to act? Assume the second block does not slide off the first block.
first, find the mass
F=ma or m=F/a
that is the original mass.
Now,
F=(m+4)a
solve for a.
To find the magnitude of the acceleration of the combination, we need to consider the forces acting on the system.
When a horizontal force of 7N acts on the first block on a resistance-free surface, it produces an acceleration of 3.5m/s^2. This means that the force applied is equal to the mass of the first block multiplied by its acceleration:
Force = Mass * Acceleration
7N = Mass1 * 3.5m/s^2
From this, we can calculate the mass of the first block (Mass1):
Mass1 = 7N / 3.5m/s^2
Mass1 = 2kg
Now, when the second 4kg block is dropped onto the first block, the force acting on the combination remains the same (7N). Since the second block does not slide off the first block, the force applied to both blocks is the same.
The total mass of the combination is the sum of the masses of both blocks:
Total mass = Mass1 + Mass2
Total mass = 2kg + 4kg
Total mass = 6kg
To find the acceleration of the combination, we can use the same formula:
Force = Total mass * Acceleration
7N = 6kg * Acceleration
Solving for acceleration:
Acceleration = 7N / 6kg
Acceleration ≈ 1.17m/s^2
Therefore, the magnitude of the acceleration of the combination is approximately 1.17m/s^2.