For some reason i cant get this question. If someone can help that would be great. Thanks.
In a pickup game of dorm shuffleboard, students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.5 kg book is pushed from rest through a distance of 0.90 m by the horizontal 25 N force from the broom and then has a speed of 1.60 m/s, what is the coefficient of kinetic friction between the book and floor?
well coeficcent are the numbers with variables close to it.kinetic friction is the moving of the object.so how many kg are in 25 newtons.so what is the 0.90 m to the 1.60 m. so with that wha do you think the answer is?
To find the coefficient of kinetic friction between the book and the floor, you'll need to use the equations of motion and the concept of work done.
First, let's break down the problem and identify the known and unknown values:
- Mass of the book (m): 3.5 kg
- Distance the book is pushed (d): 0.90 m
- Applied force (F): 25 N
- Final velocity of the book (v): 1.60 m/s
- Coefficient of kinetic friction (μ): unknown
Now, let's go through the steps to find the coefficient of kinetic friction:
Step 1: Calculate the work done by the applied force.
The work done by the force is given by the equation: work = force × distance (W = F × d).
Substituting the given values, we have:
work = 25 N × 0.90 m = 22.5 J (Joules)
Step 2: Calculate the work done by the friction force.
The work done by the friction force is given by: work = force of friction × distance (W = f × d).
Since we're trying to find the friction force, we'll rearrange the equation:
force of friction (f) = work / distance (f = W / d)
Substituting the known values, we have:
force of friction = 22.5 J / 0.90 m = 25 N
Step 3: Calculate the force of friction.
The force of friction is given by the equation: force of friction = coefficient of friction × normal force (f = μ × N).
The normal force is equal to the weight of the object (mass × gravitational acceleration): normal force (N) = m × g.
Substituting the known values, we have:
force of friction = μ × m × g
Step 4: Plug in the known values and solve for the coefficient of kinetic friction.
25 N = μ × 3.5 kg × 9.8 m/s²
Divide both sides of the equation by 3.5 kg × 9.8 m/s² to isolate the coefficient of kinetic friction (μ):
μ = (25 N) / (3.5 kg × 9.8 m/s²)
Calculating this gives:
μ ≈ 0.714
Therefore, the coefficient of kinetic friction between the book and the floor is approximately 0.714.