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Charra [1.4K]
3 years ago
12

A Smart Car, which has a mass of 1000 kg, is going 20 m/s. When it hits the barrier, it stops with a time of 0.5 seconds. What i

s the change in momentum of the car?
Physics
1 answer:
antiseptic1488 [7]3 years ago
4 0

Answer:

The change in momentum = -20000 kg m/s.

Explanation:

Mass m = 1000 kg

speed v₁ = 20 m/s

speed v₂ = 0 m/s

We know that,

The change in momentum

ΔP = m (Δv)

ΔP = m (v₂ - v₁)

     = 1000 (0 - 20)

     = 1000 (-20)

     = -20000 kg m/s

Thus, the change in momentum = -20000 kg m/s.

Note: negative sign indicates that the velocity is reducing when it hits the barrier.

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A 1-kilogram mass is attached to a spring whose constant is 21 N/m, and the entire system is then submerged in a liquid that imp
amm1812

Answer:

the required value is x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}

Explanation:

Given that,

mass, m = 1kg

spring constant k = 21N/M

damping force = -\beta\frac{dx}{dt} = \frac{-10dx}{dt}

\beta = 10

By Newtons second law ,

The diffrential equation of motion with damping is given by

m\frac{d^2x}{dt^2} = -kx-\beta\frac{dx}{dt}

substitute the value of m =1kg, k = 21N/M, and \beta = 10

1\frac{d^2x}{dt^2} = -21x=10\frac{dx}{dt}

\frac{d^2x}{dt^2} + 10\frac{dx}{dt} + 21x = 0

suppose the equation of the form x =e^m^t,

and the auxilliary equation is given by

m^2 + 10m + 21 = 0\\\\m^2 + 7m+3m+21=0\\\\m(m+7)+3(m+7)=0\\\\(m+7)(m+3)=0\\\\m=-7\\m=-3

The general solution for the above differential equation is

x(t) =C_1e^{-3t}+C_2e^{-7t}

Derivate with respect to t

x'(t)=-3C_1e^{-3t}-7C_2e^{-7t}

(a)

since time is 0 then mass is one meter below

so x(0) = 1

Also it start from rest , that implies , velocity is 0 and time is 0

x'(0) = 0

substitute the initial condition

C_1 +C_2 = 1

-3C_1-7C_2=0

Solve the above equation to get C₁ and C₂

C_1 =\frac{7}{4} and C_2 = -\frac{3}{4}

substitute for C₁ and C₂ in general solution

x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}

Thus the required value is x(t) = \frac{7}{4} e^{-3t}-\frac{3}{4} e^{-7t}

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As the man you're probably tired of hearing about said:

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