急~~這一題物理要怎麼算!

Question

題目敘述:Two rock climbers, Bill and Karen, use safety ropes of similar length. Karen's rope is more elastic, called a dynamic rope by climbers. Bill has a static rope, not recommended for safety purposes in pro climbing.

part A: Karen falls freely about 2.2 m and then the rope stops her over a distance of 1.0m . Estimate how large a force (assume constant) she will feel from the rope. (Express the result in multiples of her weight.)

求T/mg=?

part B: In a similar fall, Bill's rope stretches by only 35cm . How many times his weight will the rope pull on him?

求T/mg=?

就這樣謝謝!

我也不知道答案!

Answer 1

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Let the mass of Bill and Karen are M and m respectively.

For Karen, by equation of motion,

v2 = u2 - 2gs

v = sqrt(2gs) = sqrt(2g(2.2)) = sqrt(4.4g)

By the time the string stretches,

By v2 = u2 + 2as

0 = 4.4g + 2a(1.0)

Acceleration, a = - 2.2g

Tension, T = mg - ma = m(g + 2.2g) = 3.2mg

So, T/mg = 3.2mg/mg = 3.2

For the case of Bill,

v2 = u2 - 2gs

v = sqrt(2gs) = sqrt(2g(2.2)) = sqrt(4.4g)

By the time the string stretches,

By v2 = u2 + 2as

0 = 4.4g + 2a(0.35)

Acceleration, a = - 6.29g

Tension, T = mg - ma = m(g + 6.29g) = 7.29mg

So, T/mg = 7.29mg/mg = 7.29

Source(s): Physics king