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 4.7 kg book is pushed from rest through a distance of 0.85 m by the horizontal 42 N force from the broom and then has a speed of 1.0 m/s, what is the coefficient of kinetic friction between the book and floor

μ_k = 0.851

Explanation:

We are given;

Mass of book; m_book = 4.7 kg

Horizontal force; F_horiz = 42 N

Distance; d = 0.85 m

Speed; v = 1 m/s

First of all let's find the acceleration using Newton's equation of motion;

v² = u² + 2ad

u is initial velocity and it's 0 m/s in this case.

Thus;

1² = (2 × 0.85)a

1 = 1.7a

a = 1/1.7

a = 0.5882 m/s²

Now, resolving forces along the vertical direction, we have;

W - N = 0

Thus,W = N

Where W is weight = mg and N is normal force

Thus; N = mg = 4.7 × 9.81 = 46.107 N

Now, resolving forces along the horizontal direction, we have;

F_horiz - ((μ_k)N) = ma

Where μ_k is coefficient of kinetic friction.

Thus;

42 - 46.107(μ_k) = 4.7 × 0.5882

42 - 46.107(μ_k) = 2.76454

μ_k = (42 - 2.76454)/46.107

μ_k = 0.851

insects!

explanation:

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.