calculate the momentum of an object if:
a. its mass is 4kg and its velocity is 8m/s
b. its mass is 500g and its velocity is 3m/s
c. a force of 20N is applied to it for 6s and it moves from rest
D. its mass is 2kg and it falls from rest for 10s
(assume g = 10ms-2 or 10Nkg-1)
a. Momentum = m*V = 4 * 8 = 32.
b.0.5kg * 3m/s = 1.5.
c. m*g = 20N.
m*10 = 20
m = 2 kg.
a = F/m = 20/2 = 10 m/s^2.
V = Vo + a*t = 0 + 10*6 = 60 m/s.
Momentum = m*V = 2 * 60 = 120.
D. V = Vo + g*t = 0 + 10*10 = 100 m/s.
Momentum = m*V = 2 * 100 = 200
To calculate the momentum of an object, you can use the formula:
Momentum = mass × velocity
a. For the first scenario:
Mass = 4 kg
Velocity = 8 m/s
Momentum = 4 kg × 8 m/s
Momentum = 32 kg·m/s
So, the momentum of the object in scenario a is 32 kg·m/s.
b. For the second scenario:
Mass = 500 g = 0.5 kg (since 1 kg = 1000 g)
Velocity = 3 m/s
Momentum = 0.5 kg × 3 m/s
Momentum = 1.5 kg·m/s
So, the momentum of the object in scenario b is 1.5 kg·m/s.
c. For the third scenario:
Force = 20 N
Time = 6 s
Initial velocity = 0 m/s (starting from rest)
To calculate the momentum, we need to calculate the final velocity first.
Using Newton's second law: Force = mass × acceleration
Acceleration = Force / mass
Acceleration = 20 N / 4 kg (since mass = 4 kg for this scenario)
Acceleration = 5 m/s²
Since the object starts from rest (initial velocity = 0 m/s), we can use the equation of motion: v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
v = 0 + (5 m/s² × 6 s)
v = 30 m/s
Now, we can calculate the momentum:
Momentum = mass × velocity
Momentum = 4 kg × 30 m/s
Momentum = 120 kg·m/s
So, the momentum of the object in scenario c is 120 kg·m/s.
d. For the fourth scenario:
Mass = 2 kg
Time = 10 s
Acceleration due to gravity (g) = 10 m/s²
Using the equation of motion: s = ut + (1/2)at²
where s is the distance fallen, u is the initial velocity, a is the acceleration, and t is the time.
Since the object falls from rest, the initial velocity is 0 m/s, and the equation simplifies to: s = (1/2)at²
Using the formula for distance fallen under gravity (s):
s = (1/2)gt²
s = (1/2) × 10 m/s² × (10 s)²
s = 500 m
We can calculate the final velocity using the equation: v = u + at
where u is the initial velocity, a is the acceleration, and t is the time.
u = 0 m/s (initial velocity)
a = g = 10 m/s²
t = 10 s
v = 0 m/s + (10 m/s² × 10 s)
v = 100 m/s
Now, we can calculate the momentum:
Momentum = mass × velocity
Momentum = 2 kg × 100 m/s
Momentum = 200 kg·m/s
So, the momentum of the object in scenario d is 200 kg·m/s.