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How much force could you exert on a large crate if you wanted toget it moving? One thing the answer depends on is whether you cankeep your footing.

a) Imagine someone on level ground, pushing horizontally againsta crate, with enough effort that their feet are about to startslipping. Nevertheless, the crate hasn't started moving. What typeof force is the crate exerting on the person pushing on it, and howdoes the magnitude of this force compare to the magnitude of theforce the pusher is exerting on the crate? Explain.

b) Draw a FBD of the pusher in this situation.. Use standardsymbols for all forces, include labeled axes, and includeinformation about your velocity and acceleration. Only includeforces that act on the person pushing the crate.

c) Choose a coefficient of static friction between the pusher'sfeet (or shoes) and the floor (in the range of 0.50 to 0.70). Let'ssay the pusher's mass is 92 kg. Use N2L in conjunction with yourFBD to calculate the force exerted on the pusher by the crate whentheir feet are about to start slipping.

d) Suppose you tried this yourself – let's assume you're just asstrong as the pusher, but you weigh less. Would you be able toexert as much force on the crate as you just calculated? Why or whynot?

e) The pusher, pushing as hard as possible, manages to make thecrate start sliding, and keeps pushing. Draw a FBD for the slidingcrate.

f) Choose a coefficient of kinetic friction between the crateand the floor (between 0.30 and 0.45). Calculate the minimum time,starting from rest, it would take to push the crate 3.5 m acrossthe floor, if its mass is 71 kg. Hint: you'll need N2L and yoursecond FBD to start solving this.