If an object has a mass of 4 kg and an acceleration of 8 m/s2, what is the force this object exerts?
1 answer:
The force acting on the object will be 32 N.
Newton's second law of motion states that, "the force is equal to the change in momentum per change in the time". The mathematical form of the law is given below.
Where P = momentum, t = time, m =mass, v = velocity, a = acceleration and F = force.
The mass of the object is 4 kg and acceleration is 8 m/s^2. Substitute the values in the equation and we will get the force.
F = ma
F = 4 kg * 8 m/s^2
F = 32 kg.m/s^2
F = 32 N
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Answer:
vf₁ = 6.86 m/s , to the right
vf₂ = 2.96 m/s, to the right
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction of the velocity) and its magnitude is calculated like this:
p=m*v
where
p:Linear momentum
m: mass
v:velocity
There are 3 cases of collisions : elastic, inelastic and plastic.
For the three cases the total linear momentum quantity is conserved:
P₀ = Pf Formula (1)
P₀ :Initial linear momentum quantity
Pf : Final linear momentum quantity
Data
m₁= 0.220 kg : mass of object₁
m₂= 0.345 kg : mass of object₂
v₀₁ = 2.1 m/s ₁ , to the right : initial velocity of m₁
v₀₂= 6 m/s, to the right i :initial velocity of m₂
Problem development
We appy the formula (1):
P₀ = Pf
m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*vf₂
We assume that the two objects move to the right at the end of the collision, so, the sign of the final speeds is positive:
(0.22)*(2.1) + (0.345)*(6) = (0.22)*vf₁ +(0.345)*vf₂
2.532 = (0.22)*vf₁ +(0.345)*vf₂ Equation (1)
Because the shock is elastic, the coefficient of elastic restitution (e) is equal to 1.
1*(v₀₁ - v₀₂ ) = (vf₂ -vf₁)
(2.1 - 6 ) = (vf₂ -vf₁)
-3.9 = (vf₂ -vf₁)
vf₂ = vf₁ - 3.9
vf₂ = vf₁ - 3.9 Equation (2)
We replace Equation (2) in the Equation (1)
2.532 = (0.22)*vf₁ +(0.345)*( vf₁ - 3.9)
2.532 = (0.22)*vf₁ +(0.345)* (vf₁) -(0.345)( 3.9)
2.532 + 1.3455 = (0.565)*vf₁
3.8775 = (0.565)*vf₁
vf₁ = (3.8775) / (0.565)
vf₁ = 6.86 m/s, to the right
We replace vf₁ = 6.86 m/s in the Equation (2)
vf₂ = 6.86 - 3.9
vf₂ = 2.96 m/s, to the right