To determine the weight of the book (w book), we need to analyze the forces acting on the book in equilibrium.
The forces acting on the book are:
- The gravitational force (weight) acting vertically downward.
- The normal force acting vertically upward from the surface, perpendicular to the horizontal.
Since the book is moving at a constant velocity horizontally, the frictional force acting on it must be equal in magnitude and opposite in direction to the applied force.
Let's break down the forces acting on the book:
- Gravitational force (weight): The weight of an object can be calculated using the formula: weight = mass × acceleration due to gravity
However, since we don't have the mass of the book, we can't directly calculate the weight. Instead, we'll use the normal force to determine the weight indirectly.
- Normal force: The normal force (N) is equal in magnitude and opposite in direction to the vertical component of the applied force (10N) because the book is moving horizontally.
The vertical component of the applied force is given by: F vertical = F × sin(θ) where F is the magnitude of the applied force and θ is the angle it makes with the horizontal.
F vertical = 10N × sin(30°) F vertical = 10N × 0.5 F vertical = 5N
Thus, the normal force (N) is also 5N.
- Frictional force: The frictional force (f friction) is given by the equation: f friction = coefficient of friction × normal force
Given that the coefficient of sliding friction between the book and the horizontal surface is 0.5 and the normal force is 5N, we can calculate the frictional force: f friction = 0.5 × 5N f friction = 2.5N
Since the book is moving at a constant velocity, the frictional force must be equal in magnitude and opposite in direction to the applied force.
Therefore, the weight of the book (w book) is equal to the magnitude of the frictional force: w book = f friction w book = 2.5N
Hence, the weight of the book is 2.5N.