A diwali rocket is ejecting 50g of gases at a velocity of 400m/s find the acceleration force
Answers
Answer:20N
Explanation:
If an object moves at constant speed, its acceleration, which is the derivative of the speed with respect to time, is equal to zero.
d
d
t
(
v
)
=
a
=
0
⇔
v
=
const
The speed of the rocket is constant, but its mass is not. This implies that its momentum will not be constant.
Assuming that the rocket flies straight upward, momentum is defined as
P
=
m
⋅
v
The momentum of the rocket changes with respect to time because the mass of the rocket changes with respect to time.
According to Newton's Second Law, the rate of change of the momentum of an object is proportional to the force that's acting on it.
In your case, this force will be the ccelerating force,
F
d
d
t
(
P
)
=
d
d
t
(
m
⋅
v
)
F
=
d
d
t
(
m
⋅
v
)
Use the product rule to differentiate this function
F
=
d
d
t
(
m
)
⋅
v
+
m
⋅
d
d
t
(
v
)
=
0
This means that
F
=
v
⋅
d
d
t
(
m
)
=
50 g/s
To get the result in Newtons, convert the rate of change of the mass of the gases to
kg/s
50
g
s
⋅
1 kg
1000
g
=
0.050 kg/s
The accelerating force will thus be
F
=
400
m
s
⋅
0.050
kg
s
=
20
kg m
s
2
=
20 N