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Answer:
Vf₂ = 0.29 m/s :Speed of the block immediately after the collision.
Explanation:
Theory of collisions
Linear momentum is a vector magnitude (same direction and direction as 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 : Initial linear momentum quantity
Nomenclature and data
m₁: ball mass= 5.21 g= 5.21*10⁻³kg
V₀₁: initial ball speed, =412 m/s
Vf₁: final ball speed
m₂: block mass = 14.8 kg
V₀₂: initial block speed, = 0
Vf₂: final block speed
Problem development
For this problem the collision is perfectly elastic ,then, In addition to the linear moment, the kinetic energy is also conserved.
We assume that the ball moves to the right before the collision y continues moving to the right after the collision .(+)
We assume that the block moves to the right before the collision.(+)
We apply furmula (1)
P₀=Pf
m₁*V₀₁+m₂*V₀₂=m₁*Vf₁+m₂*Vf₂
5.21*10⁻³*412+14.8*0= 5.21*10⁻³*Vf₁+14.8*Vf₂
2.15= 5.21*10⁻³*Vf₁+14.8*Vf₂ Equation (1)
For perfectly elastic collision the coefficient of elastic restitution (e) is equal to 1, and e is defined like this:
1*(V₀₁-V₀₂) =Vf₂-Vf₁ , V₀₂=0, V₀₁ =412 m/s
412=Vf₂-Vf₁
Vf₁=Vf₂-412 Equation (2)
We replace Equation (2) in Equation (1)
2.15= 5.21*10⁻³(Vf₂-412)+14.8*Vf₂
2.15= 5.21*10⁻³*Vf₂-2.15+14.8*Vf₂
4.3=14.805Vf₂
Vf₂ =4.3/14.805= 0.29 m/s : (+) ,with equal direction of the movement of the ball before the collision.
Answer:
Explanation:
We are asked to calculate the force you are applying to a car. According to Newton's Second Law of Motion, force is the product of mass and acceleration. Therefore, we can use the following formula to calculate force.
The mass of the car is 2000 kilograms and the acceleration is 0.5 meters per second squared.
- m= 2000 kg
- a= 0.05 m/s²
Substitute the values into the formula.
Multiply.
Convert the units. 1 kilogram meter per second squared is equal to 1 Newton. Our answer of 100 kilogram meters per second square is equal to 100 Newtons.
You apply <u>100 Newtons</u> of force to the car.