Explanation:
key to this problem is the impulse-momentum theorem which states that the change in the momentum of an object is equal to the impulse applied into it.
J
=
Δ
p
,
where
J
is the impulse and
Δ
p
is the change in momentum. Basically, the impulse is the product of force and time duration, that is,
J
=
F
Δ
t
In this problem, the impulse would be the product of the force stopping the rock and
0.7
s
.
On the other hand, momentum
p
is the product of the mass
m
and velocity
v
. Therefore, the change in momentum is given by
Δ
p
=
m
2
v
2
−
m
1
v
1
.
Starting with the impulse-momentum equation, we have
J
=
Δ
p
F
Δ
t
=
m
2
v
2
−
m
1
v
1
Divide both sides by
Δ
t
,
we get
F
Δ
t
Δ
t
=
m
2
v
2
−
m
1
v
1
Δ
t
F
=
m
2
v
2
−
m
1
v
1
Δ
t
Finally, substitute the values and we get
F
=
(
2
kg
)
(
0
)
−
(
2
kg
)
(
6
m
s
)
(
0.7
s
)
F
≈
−
20
kg
m
s
2
Since
1
N
=
1
kg
m
s
2
,
then
F
≈
−
20
N
Therefore, using the correct significant figures (in this case, we need one significant figure since 2 kg, 6 m/s and 0.7 s all have one) in the final answer, we would need to have approximately
20
N
force to stop the rock in
0.7
s
.
Note: The negative sign is referring to the direction of the force opposite of the direction of the velocity
v
1
.
