UCSB Science Line
 Does the amount of stretch of a rubber band affect the distance a rubber band will travel? Question Date: 2006-11-07 Answer 1:Every child who has been in a rubber band battle instinctively knows the longer you stretch a rubber band, the farther it will go. But thy is the case involves some very fundamental ideas of physics.Determining how far something can travel is a classic problem in mechanics. Physicist would say, when released, the projectile, i.e. the rubber band, follows a ballistic trajectory. This is just a way of saying that when in flight, the rubber band is only acted upon by gravity and air resistance, and in this case, the air resistance is almost negligible.Thus, after being released, the flight path is basically determined, and the control we have are the launch angle and the initial velocity. The stretch of the rubber band only affects the initial velocity, so lets explore that in more detail.Stretching the rubber band has the same physical principles as a spring. As it is stretch, the rubber band applies a force to return to its equilibrium, or unstretched point. The amount of force can by calculated by Hooke's Law, F=k x, where k is the spring constant and x is the distance from equilibrium. The spring constant is the constant that makes the Hooke's Law mathematically correct and is usually found by experimentation. So the more the rubber band is stretched the more force it applies to return to equilibrium. So intuitively the farther you pull, the farther it should go.To quantify this intuition, we need to look at the energy. Stretching the rubber band creates a force; therefore, it's storing potential energy. The amount of potential energy it stores is given by U=1/2 k x2. In an ideal world, all of this potential energy would be converted into kinetic energy, the energy of a moving object. Since the kinetic energy is calculated by K=1/2 m v2, where m is the mass of the rubber band, the initial velocity, v, is given by v=[√ (k/m)] x. Now I did say in an ideal world, since some of the potential energy is lost to heat, but not a significant amount.So the longer you stretch the rubber band, the more initial velocity, meaning the farther it should fly assuming you keep the angle the same. Well, there is one last caveat. Rubber bands and springs have what is known as an elastic limit. If you pull it past a certain point, the physical properties of the rubber band changes, decreasing the spring constant, meaning a smaller initial velocity and a shorter distance traveled. Answer 2:That sounds like a good question for your students.If you ask them to 'vote' on the question, how many will say Yes and how many will say No? My sons junior high science teacher Mr. Winn asked a lot of questions like that.I did an experiment with a rubber band, and it landed 9 floor tiles away when I stretched it a little [9 ft] and it hit the door when I stretched it more [more than 9 ft; I didn't measure]. I'm sure your students would be delighted to do research on the question, and I'm guessing you'd rather have them do their research at home than in the classroom.The grad students and post docs in the lab discussed the question over coffee for 20 min or so and got involved with questions such as terminal velocity, where they decided that, in some cases, there might be a stretch that would make the rubber band go as far as possible, given that air resistance would slow it down; and more stretch wouldn't make it go farther. I'm not convinced, because I think if I do more work stretching the rubber band; it will travel a larger distance. The students made an interesting point: Stretching the rubber band gives it Potential Energy, like putting a rock on the top of the hill. The Potential Energy is converted to Kinetic Energy when you let go of the rubber band or push the rock so it rolls down the hill.Best wishes, Answer 3:The distance traveled DOES depend on the amount the rubber band is initially stretched. One easy way to see this is by means of an energy argument: The potential energy stored in the rubber band is proportional to the square of the stretched length. Once released, this energy is converted to kinetic energy of the rubber band, therefore, the longer it is stretched, the more kinetic energy it gets, and thus , the farther it travels. I'm assuming the holding hand is at rest during the release of the rubber band, otherwise you would need to add the mechanical work provided by the holding hand's displacement during launch. One way to verify this would be by using a(stationary) sling-shot. The farther the rubber band is stretched, the farther will the missile travel (as any 4th grade non-politically-correct squirrel hunter might attest).Click Here to return to the search form.