Question

While out on a hike you come across a stream swollen from recent rains. You need to get across it, so you decide to cross it by swinging from a vine. The vine is about 8 m in length and your speed at the bottom of the swing (as you just skim the water) is 6.00 m/s. Unknown to you, the vine has a breaking strength of 800 N. Do you make it across the river or end up taking a swim? Assume your mass is 70 kg. (You need to show stepped through calculations – Newton’s Second Law - to get credit for this). Please include a picture and/or force diagram.

Answer 1

Given that the breaking tension of the string = 800 N

The mass of our body ,m= 70 Kg

The velocity at the bottom,v = 6 m/s

The length of the string, r = 8 m

The total tension experienced by the swinging body = our weight + centrifugal force due to swinging

According to newtons 2nd law our weight

W = mg where m is the mass and g is acceleration due to gravity= 9.8 m/s²

T = mg + mv²/r

Subtituting the values,

T = 70*9.8+ 70*6²/8 = 1001 N

So the total tension experienced by the vine while swinging (1001N)is greater than the breaking tension of the vine(800N)

So it is clear that the vine will break on swinging and unfortunately we won't make up across the river,but get dropped in river.

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