Using the formula for displacement of an object calculate the following (First make a list of all the variables you have) x = vt +at? X

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Solany6426

27.04.2020

Physics

(a) v = 1.71 m/s

(b) μ = 0.005

Explanation:

(a)

Using the law of conservation of the momentum:

$m_1u_1+m_2u_2=m_1v_1+m_2v_2\\$

where,

m₁ = mass of person = 61.1 kg

m₂ = mass of sled = 16.1 kg

u₁ = initial speed of the person = 2.16 m/s

u₂ = initial speed of the sled = 0 m/s

v₁ = v₂ = v = final speeds of both the person and the sled = ?

Therefore,

$(61.1\ kg)(2.16\ m/s)+(16.1\ kg)(0\ m/s)=(61.1\ kg)(v)+(16.1\ kg)(v)\\\\v = \frac{131.976\ kgm/s}{77.2\ kg}$

v = 1.71 m/s

(b)

The kinetic energy lost by the sled must be equal to the frictional energy:

K.E = fd

$\frac{1}{2}mv^2=\mu Rd = \mu Wd\\\\\frac{1}{2}mv^2=\mu mgd\\\\\frac{1}{2}v^2=\mu g\\\\\mu = \frac{v^2}{2gd}$

where,

μ = coefficient of kinetic friction = ?

d = distance covered = 30 m

g = acceleration due to gravity = 9.81 m/s²

Therefore,

$\mu = \frac{(1.71\ m/s)^2}{(2)(9.81\ m/s^2)(30\ m)}$

μ = 0.005

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