An astronaut on a small planet wishes to measure the local value of g by timing pulses traveling down a wire which has a large object suspended from it. Assume a wire of mass 4.30 g is 1.60 m long and has a 3.00-kg object suspended from it. A pulse requires 59.9 ms to traverse the length of the wire. Calculate gplanet from these data. (You may neglect the mass of the wire when calculating the tension in it.)

2.56 m/s²

Explanation:

A standing wave is produced in the wire, its frequency f = n/2l√(T/μ). For the fundamental frequency, n = 1.

f = 1/2l√(T/μ)

where l = length of wire = 1.60 m, T₁ = tension in wire = weight of object = m₁g (neglecting wires mass), m₁ = mass of object = 3.00 kg, g = acceleration due to gravity on the small planet, μ = linear density of wire = m₀/l , m₀= mass of wire = 4.30 g = 0.0043 kg and f = 1/T where T = period of pulse = 59.9 ms = 0.0599 s

f = 1/2l√(T₀/μ) = 1/T ⇒ T₁ = 4l²μ/T²

m₁g = 4l²μ/T²

g = 4l²μ/m₁T² = 4l²m₀/l/m₁T² = 4lm₀/m₁T²

g = 4lm₀/m₁T² = 4 × 1.60 × 0.0043/(3.00 × 0.0599²) = 2.56 m/s²

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

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