A backpack full of books weighing 58.0 rests on a table in a physics laboratory classroom. A spring with a force constant of 140 is attached to the backpack and pulled horizontally.

If the backpack begins to slide when the spring ( = 140 ) stretches by 2.40 , 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 use the following equation:

μs = k / (mg)

where:
μs = coefficient of static friction
k = force constant of the spring
m = mass of the backpack
g = acceleration due to gravity

To calculate the mass of the backpack, we need to convert its weight into mass. The weight of the backpack is given as 58.0 N, and we can use the formula:

Weight = mass * acceleration due to gravity (W = mg)

So, we can rearrange the formula to solve for mass (m):

mass (m) = Weight (W) / acceleration due to gravity (g)

Next, we substitute the values into the formulas:

m = 58.0 N / 9.8 m/s^2 (acceleration due to gravity is approximately 9.8 m/s^2)

Now, we can calculate the mass:

m ≈ 5.92 kg

We are given the force constant of the spring (k) as 140 N/m and the displacement of the spring (x) as 2.40 m. The force exerted by the spring (Fs) is given by Hooke's Law:

Fs = k * x

Substituting the values:

Fs = 140 N/m * 2.40 m

Fs ≈ 336 N

Finally, we substitute the values of k, m, and g into the coefficient of static friction equation to find μs:

μs = k / (mg)

μs = (140 N/m) / (5.92 kg * 9.8 m/s^2)

Calculating μs:

μs ≈ 0.408

Therefore, the coefficient of static friction between the backpack and the table is approximately 0.408.