Two forces, one four times as large as the other pull in the same direction a 10kg mass and impart to it an acceleration of 2.5 m/s^2. if the smaller force is removed. what is the acceleration of the mass?

4/5 of the original

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To find the acceleration when the smaller force is removed, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Let's denote the larger force as F1 and the smaller force as F2. We know that the acceleration caused by the two forces combined is 2.5 m/s^2. We can set up the following equation:

F1 - F2 = m * a

where F1 is the larger force, F2 is the smaller force, m is the mass of the object (10 kg), and a is the acceleration (2.5 m/s^2).

Given that F1 is four times as large as F2, we can rewrite the equation as:

4F2 - F2 = 10 kg * 2.5 m/s^2

Simplifying the equation, we have:

3F2 = 25 kg * m/s^2

Dividing both sides by 3:

F2 = 8.33~ N

Now that we have the value for F2, we can use it to calculate the acceleration when the smaller force is removed. Since there is no longer a force opposing the motion, we only have F1 acting on the object. Therefore, the equation becomes:

F1 = m * a'

Using the value of F1 (4F2 = 4 * 8.33~ N) and the mass, we can solve for a':

4 * 8.33~ N = 10 kg * a'

a' = (4 * 8.33~ N) / 10 kg

a' ≈ 3.33 m/s^2

Therefore, when the smaller force is removed, the acceleration of the mass is approximately 3.33 m/s^2.