Question

A 62.0 kg skier is moving at 6.80 m/s on a frictionless, horizontal, snow-covered plateau when she encounters a rough patch 4.80 m long. The coefficient of kinetic friction between this patch and her skis is 0.300. After crossing the rough patch and returning to the friction-free snow, she skis down an icy, frictionless hill 2.50 m high.(a) How fast is the skier moving when she gets to the bottom of the hill?(b) How much internal energy was generated in crossing the rough patch?

Answer 1

Step-by-step explanation:

force of friction = μ mg

= .3 x 62 x 9.8

= 182.28 N

Work done by friction = 182.28 x 4.8

= 874.94 J

Energy loss by skier = 874.94 J

Kinetic energy after he passes the rough patch

= 1/2 x 62 x 6.8² - 874.94

= 1433.44 - 874.94

= 558.5 J

Velocity after crossing the patch v

1/2 x 62 x v² = 558.5

v² = 18

v = 4.2426 m /s

velocity at the bottom

v² = u² + 2gh

= 18 + 2 x 9.8 x 2.5

= 67

v = 8.18 m /s

b ) internal energy generated =

Work done by friction . = 874.94 J

Answer 2

a)
`v_f=8.186\ m.s^(-1)`

b)
`E=874.944\ J`

Step-by-step explanation:

Given:

• mass of skier,
  `m=62\ kg`

• velocity of skier on frictionless surface,
  `u=6.8\ m.s^(-1)`

• length of rough patch,
  `l=4.8\ m`

• coefficient of friction between the patch and the skis,
  `\mu=0.3`

• height of the down-hill,
  `h=2.5\ m`

a)

Frictional force acting on the rough patch while motion:

`f=\mu.N`

where:

`N=` reaction normal to the surface acting on the body

`f=0.3* (62* 9.8)`

`f=182.28\ N`

Now this force will cause deceleration in the speed if the skier and is given as:

`d=(f)/(m)`

`d=(182.28)/(62)`

`d=2.94\ m.s^(-2)`

Using equation of motion:

`v^2=u^2-2d.l`

`v^2=6.8^2-2*2.94* 4.8`

`v=4.24\ m.s^(-1)`

Now the final velocity at the bottom of the hill:

`v_f^2=v^2+2g.h`

`v_f^2=18.016+2* 9.8* 2.5`

`v_f=8.186\ m.s^(-1)`

b)

Internal energy is generated due to the kinetic frictional force and the distance covered on the patch:

(Using work-energy equivalence)

`E=f.l`

`E=182.28* 4.8`

`E=874.944\ J`