Two forces of magnitude 6N and 4N act on a body. what is the ratio of the acceleration produce when these forces are acting in the same direction to the acceleration when oppositely directed ?
f¹=6N
F=f¹+f2=10N
F=6N+4N=10N
a¹=? (10)
f²=4N
F=f¹-f²
F=6N-4N=2N
a²=? (2)
Ratio=a¹/a²
Ratio= 10/2=5
10/2
To find the ratio of the acceleration produced when the forces are acting in the same direction to the acceleration when they are oppositely directed, we can use Newton's second law of motion:
F = ma
Where F is the net force acting on the body, m is the mass of the body, and a is the acceleration produced.
When the forces are acting in the same direction, the net force is the sum of the two forces:
F_same_direction = 6N + 4N = 10N
When the forces are oppositely directed, the net force is the difference between the two forces:
F_opposite_direction = 6N - 4N = 2N
Since the mass of the body is not provided, we can assume it to be 1kg for simplicity.
Using Newton's second law, we can find the acceleration:
a_same_direction = F_same_direction / m = 10N / 1kg = 10 m/s^2
a_opposite_direction = F_opposite_direction / m = 2N / 1kg = 2 m/s^2
Therefore, the ratio of the acceleration produced when the forces are acting in the same direction to the acceleration when they are oppositely directed is:
a_same_direction / a_opposite_direction = 10 m/s^2 / 2 m/s^2 = 5.
To find the ratio of the accelerations, we need to 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. Mathematically, this can be expressed as:
F = ma
Where F is the net force, m is the mass of the object, and a is the acceleration.
Let's consider two scenarios:
1) Forces acting in the same direction:
In this case, the net force acting on the body is the sum of the two forces:
Net force = 6N + 4N = 10N
Since we know the net force, we can calculate the acceleration using the formula:
10N = ma
Now, let's consider the opposite direction scenario:
2) Forces acting in opposite directions:
In this case, the net force is the difference between the two forces:
Net force = 6N - 4N = 2N
Again, we can use the formula to calculate the acceleration:
2N = ma
To find the ratio of the accelerations, we can divide the acceleration when the forces are acting in the same direction by the acceleration when the forces are acting in opposite directions:
(10N / m) / (2N / m) = 10N / 2N = 5
Therefore, the ratio of the acceleration when the forces are acting in the same direction to the acceleration when they are acting in opposite directions is 5.