A 2-kg book is pushed along a table with a force of 4 N.
Find the frictional force on the book if the book's acceleration is 1.5 m/s\(^2\). Explain how to find the frictional force.
Answer (3)
We can use such formula F=am, where F is resultant force acting on book, a is acceleration and m is mass Now we can substitute our data. F=1.5 2
F=3 If we know that on the book is acting 4N and friction force and resultt is 3N we can create such equation 4N-Fr=3N /-4N -Fr=3N-4N -Fr=-1N / (-1) Fr=1N - its the result.
The frictional force on the book is 1 N.
To find the frictional force, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this case, the net force acting on the book is the sum of the applied force and the frictional force, which together cause the acceleration.
Given:
Mass of the book (m) = 2 kg
Applied force ( F ( a ppl i e d ) ) = 4 N
Acceleration of the book (a) = 1.5 m/s²
We can set up the equation for the net force:
F net = m ⋅ a F net = 2 kg ⋅ 1.5 m/s 2 F net = 3 N
The net force is the difference between the applied force and the frictional force:
F net = F applied − F friction 3 N = 4 N − F friction
Now, we solve for the frictional force:
F friction = 4 N − 3 N F friction = 1 N
However, this is not the final answer. We must consider that the frictional force is in the opposite direction to the applied force. Since the book is accelerating in the direction of the applied force, the frictional force must be less than the applied force by the amount of the net force. Therefore, the correct frictional force is:
F friction = F applied − F net F friction = 4 N − 3 N F friction = 1 N
But since the frictional force opposes the motion, we must take its magnitude as positive:
F friction = ∣ − 1 N ∣ F friction = 1 N
Thus, the frictional force on the book is 1 N in the direction opposite to the applied force. If we are considering the magnitude only, without direction, the frictional force is 1 N. However, if we consider the direction, the frictional force is -1 N, since it opposes the motion. In the context of the question, where only the magnitude is asked, the answer is 1 N.
The frictional force acting on the 2-kg book is 1 N. This was determined using Newton's second law, where the net force was calculated as 3 N, leading to the conclusion that the friction must counterbalance the difference between the applied force and the net force. Therefore, the friction force is 1 N.
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