Questionwith David's rope.
5.2 Newton's First Law
22. Two forces of and act on an object. Find the third force that is needed to balance the first two forces.
Studdy Solution
STEP 1
1. Two forces, and , are acting on an object.
2. The forces are given as and .
3. We need to find the third force that balances these forces, meaning the net force on the object is zero.
STEP 2
1. Understand the concept of balancing forces.
2. Calculate the resultant of the given forces.
3. Determine the third force needed to balance the resultant force.
STEP 3
Understand the concept of balancing forces.
According to Newton's First Law, an object is in equilibrium if the net force acting on it is zero. Therefore, the sum of all forces acting on the object must be zero for it to be in equilibrium.
STEP 4
Calculate the resultant of the given forces.
The resultant force is the vector sum of and :
Substitute the given forces:
STEP 5
Simplify the expression for .
First, calculate :
Now, substitute back:
Combine the terms:
STEP 6
Determine the third force needed to balance the resultant force.
The third force must be equal in magnitude but opposite in direction to to achieve equilibrium:
The third force needed is:
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