Two forces of magnitudes 6.0 N and 4.0 N act on a 3.2 kg body. What is the acceleration produced when these forces are acting in the same direction? What is the acceleration produced when these forces are oppositely directed?
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To find the acceleration produced by the two forces when they are acting in the same direction, we can use the formula:
acceleration = net force / mass
The net force in this case is the sum of the two forces:
net force = 6.0 N + 4.0 N = 10.0 N
Now we plug this into the formula:
acceleration = 10.0 N / 3.2 kg
acceleration ≈ 3.125 m/s²
Therefore, when the forces are acting in the same direction, the acceleration produced is approximately 3.125 m/s².
To find the acceleration produced when the forces are oppositely directed, we subtract the smaller force from the larger force:
net force = 6.0 N - 4.0 N = 2.0 N
Now we plug this into the formula:
acceleration = 2.0 N / 3.2 kg
acceleration ≈ 0.625 m/s²
Therefore, when the forces are oppositely directed, the acceleration produced is approximately 0.625 m/s².
To find the acceleration produced by the forces, 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.
First, let's consider the case where the forces are acting in the same direction. In this case, the net force can be obtained by adding the magnitudes of the two forces together:
Net force = 6.0 N + 4.0 N = 10.0 N
Now, using Newton's second law, we can calculate the acceleration:
acceleration = Net force / mass
acceleration = 10.0 N / 3.2 kg = 3.125 m/s²
Therefore, when the forces are acting in the same direction, the acceleration produced is 3.125 m/s².
Next, let's consider the case where the forces are oppositely directed. In this case, we need to subtract the smaller force from the larger one to obtain the net force:
Net force = 6.0 N - 4.0 N = 2.0 N
Now, we can calculate the acceleration using the net force and the mass:
acceleration = Net force / mass
acceleration = 2.0 N / 3.2 kg = 0.625 m/s²
Therefore, when the forces are oppositely directed, the acceleration produced is 0.625 m/s².
F = ma, so
together, (6.0+4.0) = 3.2a
opposite, (6.0-4.0) = 3.2a