The movie series “Back to the Future” is a classic from the 1980s about a time traveler(Marty McFly) who travels through time and embarks on adventures in the 1950s, the 2010s as well as the 19th century wild west. The DeLorean that Marty uses to time travel was built by Dr. Emmett Brown and the most important component of the car that makes time travel possible is the flux capacitor.

The first “Back to the Future” movie starts off with Marty entering Dr. Brown’s house only to find that he wasn’t there, so he turned up some knobs on a speaker and got out a guitar and played a chord only to fly backward onto a shelf(he became a projectile) and cause a wreck in Dr. Brown’s house. It seems like it is unlikely this could have happened. In order for Marty to fly backward when he played the note, there should have been a vertical force on him that was of a larger magnitude than his weight force in order for him to accelerate upwards for a small time according to Newton’s 2nd law. This net upwards force would cause Marty to accelerate upwards, but it seems impossible that this can occur because the speakers that the guitar was connected to was directly horizontal to Marty. This would mean that it would have been impossible for there to be a net upward force on Marty as the only forces acting on him vertically would be force normal and the weight force, but since the force normal and weight force cancel out, there would be no net force according to Newton’s 2nd law and thus there would be no upward acceleration.

Marty receives a message from Dr. Brown to meet him at the mall early in the morning. When Marty arrives at the mall, Dr. Brown shows his new time machine, but the Libyans somehow track Dr. Brown down and he is shot and killed. Marty takes the DeLorean and starts running from the Libyans. Since he goes above 88 mph while being chased, Marty time travels back to 1955. When Marty heads back into 1955, he runs over a scarecrow and keeps driving until he crashes into a barn. He goes into the barn with the front of the car going in first. When the owners of the barn show up to see what is going on however, the car is backward and the front of the car is facing them. In order for this to happen, there must have been a torque applied on the car that must have caused it to rotate 180 degrees. However, it was impossible for anything in this situation to provide that torque. The only thing that the car ran into as it went into the barn was a huge pile of hay. It seems impossible for the pile of hay to have provided the torque necessary to rotate the car 180 degrees. The only thing that it could do is make the car come to a stop, but not rotate it since the force applied from the hay would be applied directly at the axis of the car. The equation for torque is t = rfsin(x), where t is torque, r is radius, f is force, and x is the angle between the radius and force vectors. Since we know that the angle between the radius and the force vectors is 180 degrees as the hay has a force applied backward on the car, and if we plug in the known value of 180 degrees into the sin(x) part of the equation, since we know that sine of 180 degrees is zero, then torque is zero. This would mean that the car would not have rotated and the car should have been facing in the direction where it was headed in and it should not have been like in the movie where the car somehow had its front facing the front of the barn. We would not need to know the values of radius and force since they would be zero regardless of what their values were since sin(180) is always zero.

When Marty leaves the barn and drives away, the time of day quickly changes in a very short amount of time. Just as he speeds away from the barn, the time of day is night, but very soon right after when he reaches the middle of the street, it seems like it is noon as the sun is high up in the sky. Since the location from where he time traveled from in 1985(the mall) was close to the site of the farm and since the Hill Valley square was about 2 miles away, it seems that Marty was not driving away from the farm for a long amount of time. Let us assume and give Marty the benefit of the doubt and say that he drove away from the barn for about one hour(which is way too long considering that the distance between the farm and the street sign where it said Hill Valley was 2 miles away was very short).  We can find the period of earth’s rotation using this equation: T = 1/f where T is period and f is frequency. We multiply f on both sides and divide T on both sides to get f = 1/T. Since the period is 24 hours since this is how much time is taken to complete one full rotation of the Earth, the frequency is 1/24 (1/hr) in real life if we plug in the known variable(period) into the equation. Using this same equation, we can find the period and frequency of Earth’s rotation implied by the movie. Assuming that the sun goes from its location at 12 AM to its location at 12 PM in just one hour, we find that the period of Earth’s rotation would then be 2 hours and plugging into the equation f = 1/T, the frequency would be ½ (1/hr). It seems to be that this movie takes place on another Earth-like exoplanet with a much faster rotation!

When Marty gets to 1955, he messes up the relationship between his dad and his mom and he somehow gets them back together so that he can ensure his existence. The only problem now is that after this, he needs to get back to the year 1985, but the problem is that the DeLorean that Dr. Brown created required 1.21 gigawatts of power to travel back in time. Dr. Brown and Marty realize that they can use the power from the lightning strike on the clock tower to help get Marty back to 1985. Dr. Brown faces some problems with the wire however at the last minute and had to physically go down from the clock tower to the wires to connect them just in time for Marty to drive by and go back to 1985. It was a wonder that Dr. Brown survived the lightning strike that went through the wire he held on to in order to connect the two ends of the wires. Since voltage is V = E/q where V is voltage, E is energy, and q is charge, and since current is I = q/t, where I is current, q is charge, and t is time, we can multiply voltage and time to get that IV = E/t and since power is P = E/t, we can say that P = IV. The 1.21 gigawatts in a lightning bolt is approximately 1210000000 watts. The average lightning bolt contains about 1000000000 volts of electricity as well. Assuming that the lightning bolt that was supposed to strike the clock tower in Hill Valley did indeed produce this many gigawatts of power as well as this many volts of electricity, we can plug in these known values(voltage and power) to find the current. We get that 1210000000 = 1000000000 * I. We get that I = 1.21 A. Since 0.1 A can cause serious injuries to the human, the 1.21 A should have most likely killed Dr. Brown. 

When Marty heads back to 1985 from 1955, he tries to stop Libyans from killing Dr. Brown and when he returns to 1985, he sees the Libyan van drive by. In order to prevent the Libyans from killing Dr. Brown, Marty decides to set his destination time to about ten minutes before Dr. Brown is killed to give him time to get to the mall. Back towards the beginning of the movie when Marty enters 1955(after he time travels when he is being chased by the Libyans), there is a road sign that he sees which says that the Hill Valley town square is two miles away from the future site of the mall. This means that Marty must have run two miles in just ten minutes. Since the equation for distance is x=vt where x is distance, v is velocity, and t is time, we can find velocity by dividing t from both sides to get that v = x/t. We can then plug in the known variables(x and t) to get v. We get that v = 2/(⅙). We get that time is ⅙ since this unit is in hours and ten minutes is ⅙ of an hour. We get that Marty must have been running at an average speed of 12 miles per hour through the entire ten minutes to get to the mall and at the same time, somehow catch up to the Libyan Volkswagen hippie van! This should be an impossible feat for a nonathletic slacker like Marty to accomplish.

In “Back to the Future 2”, the film predicts that there would be hoverboards in the year 2015. After Marty successfully brings his parents back together and secures his existence, he returns to 1985 only to have Dr. Brown to take him to 2015. Marty goes into a diner in 2015 Hill Valley, and when he enters, he aggravates Griff (Biff’s grandson). When Marty gets chased by Griff, he uses a hoverboard to try to run, but it relies on Marty pushing off of the air with his foot, unlike current skateboards where you use your foot to push off the ground to accelerate. However, the problem is that the force applied by Marty’s foot is internal to the Marty-skateboard system which should not cause any acceleration to occur because of the fact that acceleration according to Newton’s 2nd law occurs whenever there is a net external force. Marty’s foot does not provide a net external force, so Marty and the hoverboard should not accelerate at all and should stay at rest since Marty and the hoverboard did not have any initial velocity. This can be seen in the equation v = at + vo in which v is final velocity, a is acceleration, t is time, and vo is initial velocity. Since we know that Marty’s foot pushing off the air is an internal force and not a net external force, Newton’s 2nd law says there is no acceleration, therefore we can plug in zero for the acceleration variable. Since vo is zero since Marty has to borrow the hoverboard from a girl on the street, who is initially at rest, we can say that the initial velocity is zero as well. Plugging in these known variables(initial velocity and acceleration), we get that Marty’s final velocity should have been zero, no matter what time we plugged in for t since no matter what value t was, the final velocity would always be zero since acceleration and initial velocity are zero. With Marty not being able to move, Marty probably would be beaten up by Griff instead of successfully being able to escape like he does in the movie.

The “Back to the Future” movie series is a classic movie that is very enjoyable to watch. Even though there are many cases in which there is bad physics as well, the errors are not blatant and do not destroy the coherence and the enjoyableness of the movie.