Question

A force of 5N, making an angle \[\theta \] with the horizontal, acting on an object displaces it by 0.4m along the horizontal direction. If the object gains kinetic energy of 1J, then calculate the horizontal component of the force.
A. 1.5N
B. 2.5N
C. 3.5N
D. 4.5N

Answer 1

Hint:Before going to solve this question we need to understand the work-energy theorem. The work-energy theorem states that work done on an object is equal to the change in the kinetic energy.

Formula Used:
To find the work done the formula is,
\[W = \overrightarrow F \cdot \overrightarrow S \]
Where, \[\overrightarrow F \] is force applied and \[\overrightarrow S \] is displacement.

Complete step by step solution:

Image: Force acting on an object.

Consider an object which is getting displaced in the horizontal direction \[S = 0.4m\]. With respect to this horizontal direction a force of 5N is acting at some angle, by this, the object is gaining 1 J of kinetic energy. Let us find the horizontal component of force. In order to do that, the F is resolved into two components that are along the horizontal direction as \[F\cos \theta \] and vertical component as \[F\sin \theta \].

According to work-energy theorem we have,
Work done = gain in the kinetic energy
\[W = 1J\]
And also by the definition of work done we have,
\[W = \overrightarrow F \cdot \overrightarrow S \]
\[W = FS\cos \theta \]
Substitute the values of W and S we get,
\[1 = F\cos \theta \left( {0.4} \right)\]
\[F\cos \theta = \dfrac{1}{{0.4}}\]
\[ \therefore F\cos \theta = 2.5N\]
Therefore, the horizontal component of force is 2.5N.

Hence, option B is the correct answer.

Note:The force that is exerted on a body consists of two components one is the horizontal component and other is vertical component. Here we are using the horizontal component of force where a force is applied in a direction parallel to the horizon.