Question

critical thinking items
8.1 linear momentum, force, and impulse

1. consider two objects of the same mass. if a force of 100 n acts on the first for a duration of 1 s and on the other for a duration of 2 s, which of the following statements is true?

a. the first object will acquire more momentum.
b. the second object will acquire more momentum.
c. both objects will acquire the same momentum.
d. neither object will experience a change in momentum.

1. cars these days have parts that can crumple or collapse in the event of an accident. how does this help protect the passengers?

a. it reduces injury to the passengers by increasing the time of impact.
b. it reduces injury to the passengers by decreasing the time of impact.
c. it reduces injury to the passengers by increasing the change in momentum.
d. it reduces injury to the passengers by decreasing the change in momentum.

Explanation:

Step1: Recall the impulse - momentum theorem

The impulse - momentum theorem states that \(J = F\Delta t=\Delta p\), where \(J\) is the impulse, \(F\) is the force, \(\Delta t\) is the time interval, and \(\Delta p\) is the change in momentum.

For the first object: \(F_1 = 100\space N\), \(\Delta t_1=1\space s\). Using \(J_1 = F_1\Delta t_1\), we have \(J_1=100\times1 = 100\space N\cdot s\)

For the second object: \(F_2 = 100\space N\), \(\Delta t_2 = 2\space s\). Using \(J_2=F_2\Delta t_2\), we have \(J_2=100\times2=200\space N\cdot s\)

Since \(J=\Delta p\), and \(J_2>J_1\), the second object has a greater change in momentum.

Step2: Analyze the car - crumple zone problem

Again, using the impulse - momentum theorem \(J = F\Delta t=\Delta p\). In a car accident, the change in momentum \(\Delta p\) of the passengers is determined by the initial and final velocities (assuming the mass of passengers is constant). The crumple zone increases the time of impact \(\Delta t\).

From \(F=\frac{\Delta p}{\Delta t}\), if \(\Delta p\) is fixed (determined by the collision kinematics), increasing \(\Delta t\) (due to crumple zone) will decrease the force \(F\) acting on the passengers.

Answer:

1. B. The second object will acquire more momentum.
2. A. It reduces injury to the passengers by increasing the time of impact.