There is something that I think is not explained well in the classic Newton Car experiment. In that experiment, a block is shot off the back of a car (using rubber bands) in one direction, causing the car to roll in the opposite direction. This experiment explains Newton’s Second Law:

Force = Mass x Acceleration

So for this experiment:

Force (of rubber band) = Mass (of Block) x Acceleration (of Block)

It also explains Newton’s Third Law of equal and opposite reaction: The action force of the block equals the reaction force exerted on the car.

Mass (of Car) x Acceleration (of Car) = Mass (of Block) x Acceleration (of Block)

There is one series of trials where the number of rubber bands are increased to create a greater force and the distance the car rolls is measured. With a greater force, the car rolls further. That is understandable. The question come about when the mass of the block is increased. In the experiment, weights are added to the block and the distance the car rolls is measured. As weights are added, the car rolls further. The explanation given is “Newton's second law states that a larger mass causes a larger force.” But why is that? My thinking is the force is really caused by the rubber band. That force remains the same. If the mass of the block is increased, the acceleration of the block should decrease according to Newton’s Second Law.

Acceleration (of Block) = Force (of rubber band) / Mass (of Block)

The force, then, on the car, should remain the same. But the experiment shows the car going further with a greater mass of the block. Why doesn’t this equation hold?

Mass (of Car) x Acceleration (of Car) = Mass (of Block) x Acceleration (of Block)

The results prove that a greater force is being exerted with a larger mass. But, since the force (the rubber band) is the same, it seemingly violates Newton’s Second Law. So something else must be going on that is not apparent. Thank you for your help.

The question come about when the mass of the block is increased. In the experiment, weights are added to the block and the distance the car rolls is measured. As weights are added, the car rolls further. The explanation given is “Newton's second law states that a larger mass causes a larger force.”

This is a mistatement of Newton's second law, which says that it takes a larger force to accelerate a larger mass to the same velocity (F=ma), but that's not what's happening here at all. It is true that the car will accelerate more with a bigger block, but the explanation has to do with conservation of energy and momentum in the system. The force in your elastic band has nothing to do with the mass of the block - it's purely dependent on how far back you stretch the rubber band. If it behaves like an ideal spring, the force in the band is equal to the distance you stretch it times the spring constant k of the band. The potential energy in the band is:


PE = \frac 1 2 k x^2


Let's assume that this is a constant - that you always pull the band back the same distance regardless of which block you're going to shoot out the back. When you release the block this potential energy is converted into kinetic energy for both the block and car:

KE = \frac 1 2 k x^2 = \frac 1 2 m_c v_c ^2 + \frac 1 2 m_b v_b ^2


Conservation of energy says that the potential energy you put into the system by stretching the band is equal to the kinetic energy that you get once the band is released.

The other effect to keep in mind is conservation of momentum:

m_b v_b + m_c v_c = 0 \\
v_b = - \frac {m_c} {m_b} v_c


Combining this with the energy equation you get:


PE = \frac 1 2 m_c v_c ^2 + \frac 1 2 m_b (- \frac {m_c} {m_b} v_c)^2 \\

PE = \frac 1 2 m_c v_c ^2 + \frac 1 2 \frac {(m_c)^2} {m_b} v_c^2 = \frac 1 2 m_c v_v^2 (1+ \frac {m_c} {m_b} ) \\
v_c^2 = 2 \times PE (\frac 1 {m_c(1+\frac {m_c} {m_b})} )


Since KE is constant (assuming for each trial you pull the rubber band back the same distance), you can see that if m_b is increased, then so is v_c .