Yes, the police can compel you to open a safe or strong box in your vehicle under certain circumstances. However, it is important to note that the specific laws and regulations regarding this issue may vary depending on the jurisdiction.

In general, law enforcement officers have the authority to conduct searches and seizures if they have probable cause to believe that the safe or strong box contains evidence of a crime or contraband. Probable cause refers to a reasonable belief, based on specific facts and circumstances, that a crime has been committed or is about to be committed.

For example, if an officer has observed suspicious behavior, received credible information, or obtained a search warrant, they may have the legal grounds to compel you to open a safe or strong box in your vehicle.

However, it is worth noting that the Fourth Amendment of the United States Constitution protects individuals from unreasonable searches and seizures. The amendment requires that searches and seizures be conducted with a warrant, based on probable cause, or under specific exceptions recognized by the courts.

One such exception is the "automobile exception," which allows law enforcement officers to search a vehicle without a warrant if they have probable cause to believe that the vehicle contains evidence of a crime. This exception is based on the notion that vehicles can be easily moved and evidence can be quickly destroyed.

Additionally, some states have enacted laws that specifically address the search of safes or strong boxes in vehicles. For example, in California, the police can compel the opening of a locked container in a vehicle if they have probable cause to believe it contains evidence of a felony offense.

It is always advisable to consult the specific laws and regulations of your jurisdiction or seek legal advice if you have concerns about your rights in relation to the opening of a safe or strong box in your vehicle.

References:

1. Cornell Law School Legal Information Institute. (n.d.). Fourth Amendment. https://www.law.cornell.edu/wex/fourth_amendment

2. FindLaw. (n.d.). Search and Seizure of Vehicles. https://criminal.findlaw.com/criminal-rights/search-and-seizure-of-vehicles.html

3. California Legislative Information. (n.d.). Section 1534 of the Penal Code. https://leginfo.legislature.ca.gov/faces/codes_displaySection.xhtml?lawCode=PEN§ionNum=1534.