Figure 5-19 gives the free-body diagram for four situations in which an object is pulled by several forces across a frictionless floor, as seen from overhead. In which situations does the acceleration
To Find
a) Which situation have x component of acceleration.
b) Which situation have y component of acceleration.
c) Direction of acceleration for each situation.
Answer to Problem 1Q
Solution
a) 2, 3 and 4.
b) 1, 3 and 4.
c) 1 – Along + y-axis, 2- Along + x-axis, 3- In 4th quadrant and 4- In 3rd quadrant.
Explanation of Solution
1) Concept:
Using the concept of net force from the Newton’s second law of motion, we can find the net force acting on the given object for given conditions.
2) Calculations:
a) According to Newton’s second law net force is product of mass and acceleration.
If we want x component acceleration there must be net force in x direction
So, For situation 1
Net force in x direction
So, there is no x component of acceleration.
For Situation 2
Net Force in x direction
As net force is 1N, x component of acceleration is present.
For Situation 3
Net Force in x direction
As net force is 1N, x component of acceleration is present.
For Situation 4
Net Force in x direction
As net force is 1N, x component of acceleration is present.
b)
For situation 1
Net force in y direction
So, there is y component of acceleration.
For Situation 2
Net Force in y direction
As net force is no y component of acceleration is present.
For Situation 3
Net Force in y direction
As net force is -1N, y component of acceleration is present.
For Situation 4
Net Force in y direction
As net force is -4N, y component of acceleration is present.
c) Direction of acceleration is in direction of net force.
For situation 1 there is only net force is only in +y direction so acceleration is also in +y direction.
For situation 2 there is only net force is only +x direction so acceleration is also +x direction.
For situation 3 as there is net force both in x and y direction and total net force is in fourth quadrant.
For situation 4 as there is net force both in x and y direction and total net force is in third quadrant.
Conclusion: Using the equations from the Newton’s second law of motion and vector algebra, it is possible to find the net force acting on the system.
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