A backpack full of books weighing 43.0 N rests on a table in a physics laboratory classroom. A spring with a force constant of 150 N/m is attached to the backpack and pulled horizontally, as indicated in the figure. If the spring stretches by 2.30 cm, what is the coefficient of static friction between the backpack and the table?
To find the coefficient of static friction between the backpack and the table, we need to first understand the forces acting on the backpack.
1. Weight (mg): The weight of the backpack, which is the force due to gravity acting on it, is given as 43.0 N.
2. Spring force (Fs): The spring is stretched horizontally, exerting a force on the backpack. This spring force depends on the displacement of the spring from its equilibrium position. In this case, the spring stretches by 2.30 cm (or 0.0230 m), and the force constant of the spring is given as 150 N/m. So, we can calculate the spring force using Hooke's Law: Fs = k * x = 150 N/m * 0.0230 m.
3. Friction force (Ff): The friction force between the backpack and the table opposes the force applied by the spring, preventing the backpack from moving horizontally. Since the backpack is at rest, the friction force equals the spring force, Ff = Fs.
Now, we can find the coefficient of static friction (μs), using the equation:
Ff = μs * N
where N is the normal force acting on the backpack. In this case, the normal force is equal to the weight of the backpack (N = mg).
Let's calculate this:
1. Calculation of the spring force (Fs):
Fs = 150 N/m * 0.0230 m
Fs = 3.45 N
2. Calculation of the friction force (Ff):
Ff = Fs = 3.45 N
3. Calculation of the normal force (N):
N = mg = 43.0 N
Finally, substitute the known values into the equation for the coefficient of static friction:
3.45 N = μs * 43.0 N
Solving for μs:
μs = Ff / N
μs = 3.45 N / 43.0 N
μs ≈ 0.0802
Therefore, the coefficient of static friction between the backpack and the table is approximately 0.0802.