A constant force acting on a body of mass 3.0 \(\text {kg}\) changes its speed from 2.0 \(\text m \, \text s^{-1}\) to 3.5 \(\text m \, \text s^{-1}\) in 25 \(\text s\). The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ?
Solution and Explanation
Mass of the body, m = 3 \(\text {kg}\)
Initial speed of the body, u = 2 \(\text m / \text s\)
Final speed of the body, v = 3.5 \(\text m / \text s\)
Time, t = 25 s
Using the first equation of motion, the acceleration (a) produced in the body can be calculated as:
v = u + at
a = \(\frac{\text v-\text u}{\text t}\)
a = \(\frac{3.5-2}{25}\)
a = \(\frac{1.5}{25}\)
a = 0.06 \(\text m / \text s^2\)
As per Newton’s second law of motion, force is given as:
F = ma
F = 3 × 0.06 = 0.18 N
Since the application of force does not change the direction of the body, the net force acting on the body is in the direction of its motion.
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Concepts Used:
Newtons Laws of Motion
Newton’s First Law of Motion:
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion:
Newton’s 2nd law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass.
Mathematically, we express the second law of motion as follows:
Newton’s Third Law of Motion:
Newton’s 3rd law states that there is an equal and opposite reaction for every action.