Two Forces Acting on an Object

• g.uricchio
You have to use the components of each vector to find the components of the other vector.In summary, you need to use the vector equation F1+F2=m*a to find the components of F2, then find the magnitude of F2 to calculate its value. Simply replacing the vectors with their magnitudes will not give you the correct answer.
g.uricchio

Homework Statement

Two forces F1 and F2 are acting on a mass m=6.0 kg. The force F1 = 7.0i + 4.0j + 3.0k, in N. The acceleration of the mass is given by a = 2.0i + 7.0j + 4.0k, in m/s2. Calculate the magnitude of F2.

F=m*a

The Attempt at a Solution

F1+F2=m*a
F2=(m*a)-F1

Magnitude of F12=72+42+32
Magnitude of F1=8.6 N

Magnitude of a2=22+72+42
Magnitude of a=8.31 m/s2

so...

shouldnt F2=(6.0 kg * 8.31 m/s2) - 8.6 N ?? (which is 41.24 N)The website where I submit my answer tells me that I am wrong please help me out.

Thankss!
--Graham

g.uricchio said:
F1+F2=m*a
F2=(m*a)-F1
This is good. Note that this is a vector equation. Use it to find the three components of F2, then find the magnitude.

Magnitude of F12=72+42+32
Magnitude of F1=8.6 N

Magnitude of a2=22+72+42
Magnitude of a=8.31 m/s2

so...

shouldnt F2=(6.0 kg * 8.31 m/s2) - 8.6 N ?? (which is 41.24 N)
You can't just replace the vectors F and a with their magnitudes.

Dear Graham,

Thank you for your explanation of your attempt at solving this problem. However, there are a few errors in your calculations.

Firstly, the magnitude of F1 is incorrect. The magnitude of a vector is calculated by taking the square root of the sum of the squares of its components. In this case, the magnitude of F1 is √(7.0^2 + 4.0^2 + 3.0^2) = √74 = 8.6 N.

Secondly, the magnitude of a is also incorrect. The magnitude of a is √(2.0^2 + 7.0^2 + 4.0^2) = √69 = 8.31 m/s^2.

Finally, when calculating the magnitude of F2, you must use the correct values for F1 and a. So, the correct equation is F2 = m*a - F1 = (6.0 kg * 8.31 m/s^2) - 8.6 N = 41.86 N.

I hope this helps clarify the correct approach to solving this problem. Keep up the good work in your studies as a scientist!

Best,

1. What is the definition of "Two Forces Acting on an Object"?

Two forces acting on an object refer to the presence of two distinct forces that are acting on an object, causing it to move or change its state of motion.

2. How do you calculate the net force of two forces acting on an object?

To calculate the net force, you need to add up all the individual forces acting on the object, taking into account both the magnitude and direction of each force. This will give you the overall force acting on the object.

3. Can two forces acting on an object be equal and opposite?

Yes, two forces acting on an object can be equal and opposite. This results in a net force of zero, causing the object to remain in a state of rest or constant motion.

4. What is the difference between balanced and unbalanced forces?

Balanced forces refer to two or more forces that are equal in magnitude and opposite in direction, resulting in a net force of zero. Unbalanced forces, on the other hand, occur when the forces acting on an object are not equal, causing the object to accelerate in the direction of the greater force.

5. How do you determine the direction of an object's motion when two forces are acting on it?

The direction of an object's motion is determined by the net force acting on the object. If the net force is in the same direction as the object's initial motion, it will continue to move in that direction. If the net force is in the opposite direction, it will cause the object to decelerate or change direction.

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