Question

critical thinking items
8.1 linear momentum, force, and impulse

1. consider two objects of the same mass. if a force of

100n 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

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.

1. how much force would be needed to cause a 17 kg·m/s

change in the momentum of an object, if the force acted
for 5 seconds?
a. 3.4n
b. 12n
c. 22n
d. 85n

Explanation:

Step1: Recall the impulse - momentum theorem

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

Step2: Calculate the impulse for each object

For the first object: \(J_1=F_1\Delta t_1\), given \(F_1 = 100\space N\) and \(\Delta t_1=1\space s\), so \(J_1=100\times1 = 100\space N\cdot s\)
For the second object: \(J_2=F_2\Delta t_2\), given \(F_2 = 100\space N\) and \(\Delta t_2 = 2\space s\), so \(J_2=100\times2=200\space N\cdot s\)

Since \(J=\Delta p\) (impulse is equal to the change in momentum), and the initial momentum of both objects is assumed to be \(0\) (not given otherwise), the momentum of the first object \(p_1=\Delta p_1 = J_1=100\space kg\cdot m/s\) and the momentum of the second object \(p_2=\Delta p_2=J_2 = 200\space kg\cdot m/s\)

Answer:

B. The second object will acquire more momentum.