A 525-g book is placed on a wooden plank which is at an angle of 35.0° to the horizontal. After the book is released, it is measured to slide down the plank with an acceleration of 2.56 m/s2.
(a) Calculate the coefficient of kinetic friction between the book and the plank.
(b) If the book was released from rest, calculate the work done by gravity after it has moved
down the plank a distance of 55.0 cm.
(c) If the book was released from rest, calculate the work done by friction after it has moved
down the plank a distance of 55.0 cm.
M*g = 0.525 * 9.8 = 5.15 N. = Wt. of book.
Fp = 5.15 * sin35 = 2.95 N. = Force in-parallel with plank.
Fn = 5.15*Cos35 = 4.21 N. = Normal force or force perpendicular to plank.
a. Fp - Fk = M*a.
2.95 - Fk = 0.525 * 2.56,
Fk = 1.61 N. = Force of kinetic friction.
Fk = u*Fn = 1.61.
u * 4.21 = 1.61,
u = ?
b. W = Mg * d = 0.525 * 0.55 =
c. W = Fk * d =
To solve this problem, we'll need to use the concept of forces and work. Here's how we can find the answers to each part of the question:
(a) To calculate the coefficient of kinetic friction between the book and the plank, we need to consider the forces acting on the book as it slides down the plank. The main forces involved are the force of gravity (mg) acting vertically downwards and the force of kinetic friction (f) acting parallel to the plank's surface.
The force of gravity can be determined using the mass of the book (m = 525 g = 0.525 kg) and the acceleration due to gravity (g = 9.8 m/s^2). Therefore, the force of gravity (FG) is given by FG = mg.
Next, we need to determine the force of kinetic friction. Since the book is sliding down the plank, the force of friction is the only horizontal force acting against the motion. We can find the force of friction (f) using the equation f = μN, where μ is the coefficient of kinetic friction and N is the normal force.
The normal force (N) is the component of the force of gravity that acts perpendicular to the plank's surface. It can be calculated as N = mg cosθ, where θ is the angle between the plank and the horizontal.
Using the known values, we can calculate the normal force and the force of friction. Once we have the force of friction, we can substitute it into the equation f = ma, where a is the acceleration, to solve for the coefficient of kinetic friction (μ).
(b) To calculate the work done by gravity after the book has moved down the plank a distance of 55.0 cm, we need to determine the gravitational force acting on the book (FG) and the displacement (d).
First, convert the distance from centimeters to meters by dividing by 100. Then, use the formula for the work done by a constant force: work (W) = force (F) × displacement (d) × cos(θ), where cos(θ) is the cosine of the angle between the force and the displacement.
In this case, the force is the force of gravity (FG), and the displacement is the distance the book has moved down the plank (d = 55.0 cm converted to meters). Plug the values into the formula to find the work done by gravity.
(c) To calculate the work done by friction after the book has moved down the plank a distance of 55.0 cm, we need to determine the force of friction (f) and the displacement (d).
The work done by friction is given by the formula W = f × d × cos(θ), where f is the force of friction and d is the displacement.
Using the previously calculated force of friction (f) and the distance the book has moved down the plank (d = 55.0 cm converted to meters), we can find the work done by friction using the formula.
By following these steps and plugging in the appropriate values, you should be able to find the answers to each part of the question.