A student puts a 0.80 kg book against a vertical wall and pushes the book toward the wall with a force of 26N [R]. The book does not move.
a) calculate the minimum coefficient of static friction.
b) describe two ways the student could make the book accelerate down without changing the applied force.
A student places a ladder up against a wall as shown below. The normal force applied by the wall on the ladder will be directed:
0.30
0.30
To calculate the minimum coefficient of static friction (μs), we need to consider the forces acting on the book and use the equilibrium conditions.
Let's break down the forces acting on the book:
1. Weight (W): The force due to gravity pulling the book downward. The weight of an object can be calculated using the formula W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s²).
Given that the mass of the book is 0.80 kg, the weight of the book is W = 0.80 kg * 9.8 m/s² = 7.84 N (directed downward).
2. Applied force (F_applied): The force applied by the student in an attempt to move the book. In this case, it has a magnitude of 26 N and is directed to the right (R).
3. Normal force (N): The force exerted by the wall perpendicular to the book. This force counteracts the weight of the book and balances it out. Since the book is not moving vertically, the normal force is equal in magnitude and opposite in direction to the weight force. Therefore, the normal force is N = 7.84 N (directed upward).
Now, let's use the equation for static friction: F_friction = μs * N, where F_friction is the force of static friction.
Since the book does not move, the applied force must equal the force of static friction:
F_applied = F_friction
Therefore, we can calculate the minimum coefficient of static friction (μs) by rearranging the equation:
μs = F_friction / N = F_applied / N
Substituting the given values:
μs = 26 N / 7.84 N = 3.32
So, the minimum coefficient of static friction (μs) is approximately 3.32.
Now, let's move on to describing two ways the student could make the book accelerate down without changing the applied force:
a) Decrease the coefficient of static friction (μs): The student can accomplish this by changing the surface against which the book is being pushed. For example, if the book were originally pushed against a wall with a rough texture, the student could switch to a smoother surface, reducing the static friction and allowing the book to accelerate downward.
b) Decrease the normal force (N): The student can achieve this by changing the angle at which the book is being pushed against the wall. By tilting the book slightly, the effective normal force would decrease, reducing the static friction and enabling the book to accelerate down. However, it’s important to note that tilting the book would also affect the applied force required to push it.