Final answer:
The greatest force P that can be applied without causing the crate to move, considering a coefficient of static friction of 0.45, is 2205 N, which is calculated using the maximum static frictional force formula fs(max) = μsN.
Step-by-step explanation:
The question relates to the topic of static and kinetic friction in physics, specifically regarding the force required to move a crate on a dolly. The student asks to determine the greatest force that can be applied without causing motion to a 500 kg crate resting on a dolly, given that the coefficient of static friction (μs) is 0.45. The maximum static frictional force (fs (max)) can be calculated using the equation fs (max) = μsN, where N is the normal force. Given that the crate has a mass of 500 kg and assuming gravity (g) is 9.80 m/s², the normal force is N = mg = (500 kg)(9.80 m/s²) = 4900 N. Thus, the maximum static frictional force that can be applied is fs (max) = (0.45)(4900 N) = 2205 N. This means that a force up to 2205 N can be applied without causing the crate to move. However, remember that the question may contain specific details about the setup that could influence the answer, such as the orientation of the force or additional forces acting on the crate.