The forces in (Figure 1) are acting on a 3.0kg object.
Part A
What is ax, the x-component of the object's acceleration?
Express your answer to two significant figures and include the appropriate units
ax = |
The required concepts to solve the given problem are Newton’s second law of motion, and the vectors.
First, calculate the component of force acting on the object from the diagram. Then use Newton’s second law of motion to find the acceleration of the object along the direction.
Force may be defined as the sudden push or pull which is capable of changing the direction of the object.
Newton’s second law states that the acceleration of an object produced by a net force is directly proportional to the magnitude of net force and inversely proportional to the mass of the object.
Expression for force acting on an object is,
Here, is the force acting on the object, is the mass and is its acceleration.
A vector is a quantity that has both magnitude and direction. Force is a vector quantity. It has both magnitude and direction. Direction of force is same as that of the direction of acceleration.
Acceleration of the object is,
The component of acceleration is,
Here, is the mass of the object, is the component of acceleration and is the component of force.
(A)
Consider the given diagram. Here, force is acting along the positive and negative directions. Let represents the positive side of the axis and represents the negative side of the axis.
From the diagram, component of force acting on the object is,
Here, is the force acting along the positive axis and is the force acting along the negative axis.
Substitute for and for .
The component of acceleration is,
Substitute for and for .
Ans: Part AThe component of acceleration is .
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