Answer:
Impulse = 48 kg m/s
Gain in momentum = 48 kg m/s
Explanation:
Force (F) = 6N
Time (t) = 8
Mass (m) = 3 kg
Final velocity (v) = ?
Initial velocity (u) = 0 m/s
First, find acceleration
F = m * a
a = F / m
a = 6 / 3
a = 2 m/s^2
Now, find final velocity
v = u + a * t
v = 0 + 2 * 8
v = 16 m/s
Now, find impulse
Impulse = change in momentum
Impulse = final momentum - initial momentum
Impulse = m * v - m * u
Impulse = m ( v - u )
Impulse = 3 ( 16 - 0 )
Impulse = 48 kg m/s
Here, gain in momentum is same as impulse.
a) The impulse is 48 Ns
b) The momentum the object gained is 48 kgms⁻¹
From the question,
We are to calculate the impulse
Impulse can calculated by using the formula,
I = Ft
Where
I is the impulse
F is the force
and t is the time
From the given information,
F = 6 N
t = 8 secs
Therefore,
I = 6 × 8
I = 48 Ns
The impulse is 48 Ns
b) To determine how much momentum the object gained.
Momentum is given as by the product of mass and change in velocity.
That is,
Momentum = m(v -u)
Where
m is the mass
v is the final velocity
and u is the initial velocity
From Sir Isaac Newton's second law of motion equation, we have that
F = ma
Where F is the force
m is the mass
and a is the acceleration
But, acceleration, a, is given by
[tex]a = \frac{v-u}{t}[/tex]
Therefore, the equation becomes
[tex]F = m\frac{(v-u)}{t}[/tex]
This can be written as
[tex]Ft = m(v-u)[/tex]
Since, I = Ft
Then,
[tex]I = m(v-u)[/tex]
This means
Impulse = Momentum
Thus,
The momentum the object gained is 48 kgms⁻¹
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