10. Someone takes 11 minutes to walk up a hill 120m high. His weight is 550N.

(a) How much work did he do in climbing the hill?

(b) How many seconds did he take to climb the hill?

(c) What power is developed by his muscles as he climbs?

(d) If he runs up the hill his muscles can exert 500 Watts. How long will it take him to get to the top of the hill?

Question

03-01-2022
Physics

Answered

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10. Someone takes 11 minutes to walk up a hill 120m high. His weight is 550N.

(a) How much work did he do in climbing the hill?

(b) How many seconds did he take to climb the hill?

(c) What power is developed by his muscles as he climbs?

(d) If he runs up the hill his muscles can exert 500 Watts. How long will it take him to get to the top of the hill?

Sagot :

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moya1316 moya1316 · Answer 1 · 2022-01-17T06:30:18-05:00

The relationship between work and kinetic energy and the definition of power allows to find the results for the questions about the climb of the mountain are:

a) The work is: W = 6.47 10⁵ J

b) The time is: t = 660 s

c) The power es: P = 980 W

d) The time is: t = 1.18 10³ s

Work and energy relationship.

The work is defined by the scalar product of force and distance and is equal to the change in kinetic energy.

W = ΔK.

Where W is work and K is kinetic energy.

a) Let's use the conservation of energy between the base of the hill and the height.

Starting point. Lower part of the hill.

Em₀ = K

Final point. The highest part of the hill

Em_f = U = m g h

We assume that it starts from rest in the lower part.

The energy is conserved .

Em₀ = Em_f

K = mgh

We substitute at work,

W = U- 0

W = 550 9.8 120

W = 6.47 10⁵ J

b) Indicate the time it took to climb the hill t = 11 minutes. Let's reduce to seconds.

t = 11 min ( [tex]\frac{60s}{1 min}[/tex] )

t = 660 s

Power definition.

c) The power at work per unit of time.

P = [tex]\frac{W}{t}[/tex]

P = [tex]\frac{6.47 \ 10^5 }{660}[/tex]

P = 980 W

d) The work to get to the top of the hill does not depend on time.

t= [tex]\frac{W}{P}[/tex]

t = [tex]\frac{6.47 \ 10^5}{ 550}[/tex]

t = 1.18 10³ s

In conclusion, using the relationship between work and kinetic energy and the definition of power, we can find the results for the questions about the climb of the mountain are: