07 Pulling a Slackened Rope

Aim

To show that only a short impulse is needed to make a student move.

Subjects

• 1N20 (Conservation of Linear Momentum)

Diagram

Fig. 173 .

Equipment

• Two light carts, easily rolling.

• Rope; \(l=10\mathrm{~m}\).

• Two students.

Presentation

The two students stand each on a cart. Between them is a slackened rope. Slowly they increase the tension in the rope and at a certain moment both carts start moving towards each other. The rope slackens again, but both carts keep on moving. (Eventually friction will stop their movement.)

When there is a clear mass difference between the two students, the difference in their respective speeds will be clearly observable.

Explanation

The tension in the rope implies an impulse \(F \Delta t\) to the cart + student. This impulse changes the momentum \(p=m_{1} \Delta v_{1}\) of the cart + student. Applying Newton’s second law we can say: \(F \Delta t=m_{1} \Delta v_{1}\). When the initial velocity is zero, then \(m_{1}\) will move with \(v_{1}\) after the short impulse is over.

Applying ‘conservation of linear momentum’ to the whole system it is clear that the change of momentum of \(m_{2}\) is \(-\Delta p=m_{2} \Delta v_{2}\). \(v_{2}\) will be opposite to \(v_{1}\) and when \(m_{2}>m_{1}\), \(v_{2}\) will be lower than \(v_{1}\).

Sources

• Mansfield, M and O’Sullivan, C., Understanding physics, pag. 122-123