Problem 2
Answer: Choice D only
Explanation:
Let's go through the list of possible answers
- A) She only would feel a force pulling her toward the chair, hence making her feel heavier, only when the space ship is accelerating faster. In this case, she is moving a constant speed of 0.5c (aka half the speed of light). Despite going this fast, she is moving at a constant speed and therefore not accelerating at this current time. The speed isn't changing. Therefore, she would not feel a force pushing her into the chair. Choice A is off the list.
- B) This is also off the list as well. The lack of accelerating force means her lungs aren't compressed and breathing should be normal. This is assuming she doesn't have any medical conditions hindering her breathing. We can cross choice B off the list.
- C) This is similar to choice B. We can cross it off the list.
- D) The faster you go, the more time dilation will occur. This effectively compresses time and makes it slow down. The more detailed explanation involves relativity which is very complicated. Therefore, choice D is the answer.
- E) This is false because choice D was mentioned to be true.
When the box IS on the shelf 2m above the ground,
its potential energy is
(weight) x (height) = (3 N) x (2 m) = 6 joules .
THAT's the work you have to do, to lift the box up to there.
Answer: 24.5 cm
Explanation:
Given
Force constant of spring, k = 40 N/m
Diameter of spring, d = 5.1 cm = 0.051 m
Mass of cylinder, m = 1.5 kg
Let us assume that the cylinder is hanging in such a way that the circular end is parallel with the water. Also, we assume that the tank water level is not materially affected by the displacement of the cylinder while the cylinder sinks. The water is fresh and as we all know, the density of water is 1000 kg/m³
To solve this, we assume x to be the spring extension and it's equivalent sinking distance(in meters). We then apply the formula,
mg = kx + ρgAx
mg = x(k + ρgA)
x = mg / (k + ρgA), where
A = πd²/4
A = (3.142 * 0.051²)/4
A = 0.0082 / 4
A = 0.00205 m²
x = 1.5 * 9.81 / [40 + (1000 * 9.81 * 0.00205)]
x = 14.715 / (40 + 20.1105)
x = 14.715 / 60.1105
x = 0.245 m
or 24.5 cm of stretch or sinking