In the figure a fastidious worker pushes directly along the handle of a mop with a force upper f overscript right-arrow endscripts. the handle is at an angle θ = 44° with the vertical, and μs = 0.68 and μk = 0.32 are the coefficients of static and kinetic friction between the head of the mop and the floor. ignore the mass of the handle and assume that all the mop's mass m = 0.64 kg is in its head.
(a) if the mop head moves along the floor with a constant velocity, then what is f?
(b) if θ is less than a certain value θ0, then upper f overscript right-arrow endscripts (still directed along the handle) is unable to move the mop head. find θ0.

Conceptualize notice how this problem differs from our previous discussion of gauss's law. the electric field due to point charges was discussed in the previous section. now we are considering the electric field due to a distribution of charge. we found the field for various distributions of charge in the chapter entitled electric fields by integrating over the distribution. this example demonstrates a difference from our discussions in the previous chapter. in this chapter, we find the electric field using law. categorize because the charge is distributed uniformly throughout the sphere, the charge distribution has spherical symmetry and we can apply gauss's law to find the field. analyze note that the following conditions can be used to determine a suitable gaussian surface. condition (1): the value of the electric field can be argued by symmetry to be constant over the portion of the surface. condition (2): the dot product e â· da can be expressed as a simple algebraic product e da because e and da are parallel.