Question

Matthew starts from rest on top of 8.45 m high sledding hill. He slides down the 32-degree incline and across the plateau at its base. The coefficient of friction between the sled and snow is 0.128 for the plateau and the hill is frictionless. Matthew and the sled have a combined mass of 27.5 kg. Determine the distance which Matthew will slide along the level surface of the plateau before coming to a complete stop.

Answer 1

Answer:

S = 52.5 m

Explanation:

given,

height of the sledding hill = 8.45 m

angle of inclination = 32°

coefficient of friction of sled = 0.128

Mathew and sled have combined mass = 27.5 Kg

using energy conservation equation

Applying energy conservation

 $E_a = E_b + w_f$

 $m g h= \dfrac{1}{2}mv_b^2 + f\ l$

 $\dfrac{1}{2}mv_b^2= m g h -f\dfrac{h}{sin\theta}$

  f = μ N

  f = μ m g cos θ

 $\dfrac{1}{2}mv_b^2= m g h -\mu mg cos\theta \dfrac{h}{sin\theta}$

 $\dfrac{1}{2}mv_b^2=m g h(1 -\mu cot\theta)$

 $\dfrac{1}{2}mv_b^2=27.5 \times 9.8 \times 8.45 (1 -0.128 \times cot 32^0)$

 $\dfrac{1}{2}mv_b^2=1810.8\ J$

distance cover on the flat surface be s

  $\dfrac{1}{2}mv_b^2=\mu m g S$

  $\mu m g S= 1810.8$

  $S= \dfrac{1810.8}{\mu m g}$

  $S= \dfrac{1810.8}{0.128 \times 27.5 \times 9.8}$

        S = 52.5 m

Answer 2

The distance which Matthew will slide along the level surface of the plateau is 52.5 m.

Conservation of energy

The kinetic energy of Mathew is determined by applying the principle of conservation of energy.

K.E = ΔP.E

K.E = mgh - Fl

K.E = mgh - μmgcosθ x h/sinθ

$K.E = mgh(1 - \mu cot\theta)\\\\K.E = 27.5 \times 9.8 \times 8.45( 1 \ - \ 0.128\times cot32)\\\\K.E = 1810.79 \ J$

Distance traveled by Mathew along the surface

μmgx = 1810.79

x = 1810.79/(μmg)

x = 1810.79/(0.128 x 27.5 x 9.8)

x = 52.5 m

Learn more about conservation of energy here: https://brainly.com/question/166559