# Can velocity change without any component of acceleration in opposite direction of motion?

If a truck of mass 100kg is moving with some velocity say 10m/s ( pls assume friction is negligible but still truck is moving)when suddenly an object of mass 10kg falls on it from above and stickes to it ,such that the object has 1m/s speed (say) in the downward direction when it was about touch the truck. Now the velocity of the system decreases a/c law of conservation of momentum. But if change in velocity has to occur, there must be an acceleration in the opposite direction of the motion of the truck, but since this is an isolated system no external force is possible. Only forces acting are internal forces btw object and truck in the perpendicular direction to the motion of truck. How did the velocity change without any component of acceleration in the opposite direction of the truck?

Pls clear my confusion!!!!! Thank you

After the $$10$$ kg mass falls onto the truck here must some force acting on it to prevent it sliding straight off the back of the truck. This could be friction, or it could hit a wall at the back of the truck. In any case, the truck is exerting some force on the $$10$$ kg mass to increase its horizontal sped from $$0$$ to $$10$$ m/s. By Newton's Third Law the $$10$$ kg mass exerts an equal and opposite force on the truck which slows the truck down (assuming there is no driving force maintaining the truck's speed).

• Just a note - even an object would bump of the truck due to ricochet, for induced temporary increase in normal force,- rolling friction would increase resulting in negative acceleration. – Agnius Vasiliauskas Oct 12 '20 at 9:16

Can velocity change without any component of acceleration in opposite direction of motion?

Simple answer is NO, it can't. Falling object induced a change in rolling friction force :

\begin{align} \Delta F&=C_{rr}\Delta N \\&=C_{rr}~m_o\left(\frac{v_i}{\Delta t}+g\right) \end{align}

Where $$m_o$$ is falling object mass, $$v_i$$ is object impact speed, $$\Delta t$$ impact duration. So object increases rolling resistance and as such - produces negative acceleration, due to friction change.

EDIT

Complex answer is, in some cases it can. For example if an object is rotating in a circular motion due to some centripetal force, then lowering centripetal acceleration for an object at a fixed radius, it's tangential speed perpendicular to centripetal acceleration vector will drop too. But your example is about movement in a straight trajectory, so this is not the case here.

• What about the force to accelerate the mass horizontally? – Adrian Howard Oct 12 '20 at 9:21
• What do you mean ? – Agnius Vasiliauskas Oct 12 '20 at 9:25
• The mass has only downward speed, it lands in the truck, the truck accelerates the mass, the mass negatively accelerates the truck. – Adrian Howard Oct 12 '20 at 10:10
• Can be, just this does not depend on object downward momentum. In reality the bigger object impact speed - higher deceleration truck will get due to bigger rolling friction induced. Thus your explanation is good, but not enough to account all effects. – Agnius Vasiliauskas Oct 12 '20 at 11:29
• except it is stated friction is negligible – Adrian Howard Oct 12 '20 at 12:06