A force of 40 N is required to start a 5 kg box moving across a horizontal concrete floor. (a) What is the coefficient of static friction between the box and the floor? (b) If the 40 N force continues, the box accelerates at 0.70 m/s2. What is the coefficient of kinetic friction?

To find the coefficient of static friction (µs), we can use the equation:

µs = F_static / N

where:
- F_static is the force required to start the box moving (40 N)
- N is the normal force, which is equal to the weight of the box (mass x gravity)

(a) Calculating the coefficient of static friction:
Since the box is on a horizontal floor, the normal force is equal to the weight of the box, which can be calculated as:

N = mass x gravity
N = 5 kg x 9.8 m/s^2
N = 49 N

Now, we can find the coefficient of static friction using the equation:

µs = F_static / N
µs = 40 N / 49 N
µs ≈ 0.82

Therefore, the coefficient of static friction between the box and the floor is approximately 0.82.

(b) To find the coefficient of kinetic friction (µk), we can use the equation relating it to acceleration:

µk = F_kinetic / N

where:
- F_kinetic is the force required to maintain constant acceleration (40 N)
- N is still the normal force (equal to the weight of the box)

Throughout the motion, the force of friction opposes the applied force, so the force exerted by the friction is equal to the force applied:

F_kinetic = F_applied

Hence, we can use the equation:

F_kinetic = mass x acceleration

Plugging in the given values:

40 N = 5 kg x 0.70 m/s^2

Now, we can calculate the kinetic friction force:

F_kinetic = mass x acceleration
F_kinetic ≈ 3.5 N

Finally, we can find the coefficient of kinetic friction:

µk = F_kinetic / N
µk = 3.5 N / 49 N
µk ≈ 0.071

Therefore, the coefficient of kinetic friction between the box and the floor is approximately 0.071.