boy pushes a 3.3-kg book against a vertical wall with a horizontal force of 43 N. What is the minimum coefficient of friction that will keep the book in place without sliding
Fap-Ff = m*a.
43-Ff = 3.3*0 = 0
Ff = 43 N. = Force of friction.
To find the minimum coefficient of friction that will keep the book in place without sliding, we need to take into account the force applied by the boy and the force of friction.
Let's break down the forces acting on the book:
1. Normal force (Fn): The force exerted by the wall on the book, perpendicular to the surface. Since the book is not moving vertically, the normal force is equal to the weight of the book, which can be calculated using the formula:
Fn = m * g,
where m is the mass of the book and g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the values:
Fn = 3.3 kg * 9.8 m/s^2 = 32.34 N.
2. Force applied by the boy (F): The force the boy is pushing the book horizontally with, which is given as 43 N.
3. Force of friction (Ff): The force acting parallel to the surface between the book and the wall, opposing the force applied by the boy.
In order to calculate the minimum coefficient of friction, we need to determine the maximum force of friction, which occurs when the book is on the verge of sliding. The maximum force of friction can be calculated using the equation:
Ff = μ * Fn,
where μ is the coefficient of friction.
Since we're looking for the minimum coefficient of friction, we'll set the force of friction equal to the applied force by the boy:
Ff = F = 43 N.
Now we can solve for the coefficient of friction (μ):
μ * Fn = 43 N,
μ * 32.34 N = 43 N,
μ = 43 N / 32.34 N,
μ ≈ 1.33.
So, the minimum coefficient of friction that will keep the book in place without sliding is approximately 1.33.