why do astronauts build radio telescopes and x-ray telescopes, in addition to the optical telescopes with which most people are
1 answer:
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Answer:
His kinetic energy increases, potential energy decreases
The sum of kinetic and potential energy is a constant at any instant before he comes to rest.
Explanation:
Snowboarder is starting from a height and moving to the down direction. As he moves down his velocity increases, we know that kinetic energy is given by the expression , so as he moves his kinetic energy increases.
When the snowboarder is starting his potential energy is maximum(Potential energy = mgh), as he comes down his potential energy decreases.
Based on this we can conclude that the sum of potential energy and kinetic energy is a constant at any instant for a snowboarder before he comes to rest.
mgh+= Constant
Answer:
The tension in each half of the rope, is approximately 4,908.8 N
Explanation:
The mass of the acrobat, m = 60 kg
The length of the rope, l = 10 m
The extent by which the center dropped = 30 cm = 0.3 m
Let, 'T' represent the tension in each half of the rope
Weight, W = Mass, m × The acceleration due to gravity, g
∴ W = m × g
The acceleration due to gravity, g ≈ 9.8 m/s²
∴ The weight of the acrobat, W = 60 kg × 9.8 m/s² ≈ 588 N
The angle the dropped rope makes with the horizontal, θ is given as follows;
θ = arctan((0.3 m)/(5 m)) = arctan(0.06) ≈ 3.434°
At equilibrium, the sum of vertical forces, = 0
The vertical component of the tension, , in each half of the rope is given as follows;
= T × sin(θ)
∴ = W + T × sin(θ) + T × sin(θ) = W + 2 × T × sin(θ)
Plugging in the values, with θ = arctan(0.06) for accuracy, we get;
588 N + 2 × T × sin(arctan(0.06) = 0
∴ 2 × -T × sin(arctan(0.06) = 588 N
-T= 588 N/(2 × sin(arctan(0.06)) = 4,908.81208 N ≈ 4,908.8 N
The tension in each half of the rope, T ≈ 4,908.8 N.
