Stepping onto the Dock — Why the Boat Moves Back
A small wooden rowing boat lies stern-first against a stone quay, resting on a hanging tyre fender, and a person stands in the stern ready to step off. Nobody pushes the boat, yet as the person steps onto the quay it slides backward and the gap of water widens. Three sliders set the person's mass, how fast they step off and the mass of the boat with its cargo (crates of 20 kg each). Press play to watch the whole step once, at real speed: the back foot pushing on the boat, the front foot swinging onto the quay, the boat recoiling and water drag slowing it down. Drag the timeline to any moment to look again.
Como usar esta simulação
- Person's mass m — 40 to 100 kg, starting at 60 kg. The figure is drawn a little taller for a heavier person.
- Stepping speed v — 0.5 to 2.5 m/s, starting at 1.50 m/s: how fast the person is moving when the back foot leaves the boat.
- Boat + cargo M — 60 to 260 kg in steps of 20 kg, starting with the empty 60 kg boat; each extra 20 kg appears as a wooden crate. A change keeps the timeline where it is.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion.
- Drag anywhere on the scene to look around.
O que observar
- During the push-off the two momentum arrows grow together and always have the same length: at the start values they end at +90 and −90 kg m/s, and the total stays 0.
- At ⅛× watch the push-off: the front foot swings over the stern onto the quay while the back foot, still on the boat, rolls onto its toes and pushes the boat away.
- The empty 60 kg boat recoils at 1.50 m/s, as fast as the person steps off; loaded to 220 kg it moves off at only 0.41 m/s. During the push the empty boat slides back 23 cm while the person moves 23 cm forward; the loaded boat slides back only 10 cm.
- A 100 kg person stepping off at 2.5 m/s sends the empty boat back at 4.17 m/s; a 40 kg person stepping gently at 0.5 m/s barely moves a 260 kg boat, 0.08 m/s.
- After the push-off water drag takes over: two seconds later the empty boat's momentum has fallen from −90 to about −45 kg m/s, while the person stands still on the quay.
A física por trás
Take the person and the boat as one system, with towards the quay as the positive direction. Before the step everything is at rest, so the total momentum is 0. During the push-off the only horizontal forces are the ones the back foot and the boat exert on each other: equal in size, opposite in direction and acting for the same time, so they give equal and opposite impulses and p(person) + p(boat) stays 0. If the person leaves at speed v, the boat must take −mv, so its recoil velocity is V = −mv/M. With 60 kg stepping off at 1.50 m/s the person carries +90 kg m/s, and an empty 60 kg boat recoils at −90/60 = −1.50 m/s; loaded to 220 kg, the same step gives it only −0.41 m/s. The push-off lasts as long as the back leg can extend, 0.30 s at these values. The water's sideways push during that short time is negligible; afterwards water drag is a force from outside the system, so the boat's own momentum drains away.