Answer:
C
Explanation:
In this pair of graph we have the displacement versus time graph as concave up and if we consider it to be parabolic function then as we know that the velocity is given by the slope of the displacement-time graph.
where:
s= displacement
t= time
We get the linear inclined slope graph of the velocity versus time graph which stands true if we differentiate a parabolic function.
Also observe that at time t=0 we have slope of displacement graph as zero so corresponding to it we get velocity as zero in the velocity graph.
For this case we have that by definition:
Where,
We have then:
Then, by clearing the acceleration we have:
Substituting values we have:
Answer:
The acceleration of the box is equal to:
To solve this problem it is necessary to apply the concepts related to the heat flux rate expressed in energetic terms. The rate of heat flow is the amount of heat that is transferred per unit of time in some material. Mathematically it can be expressed as:
Where
k = 0.84 J/s⋅m⋅°C (The thermal conductivity of the material)
Area
Length
= Temperature of the "hot"reservoir
= Temperature of the "cold"reservoir
Replacing with our values we have that,
Therefore the correct answer is B.
Answer:
82.76m
Explanation:
In order to find the distance of the steel ring to the ground, when its temperature has raised by 1°C, you first calculate the radius of the steel tube before its temperature increases.
You use the formula for the circumference of the steel ring:
(1)
C: circumference of the ring = 40000 km = 4*10^7m (you assume the circumference is the length of the steel tube)
you solve for r in the equation (1):
Next, you use the following formula to calculate the change in the length of the tube, when its temperature increases by 1°C:
(2)
L: final length of the tube = ?
Lo: initial length of the tube = 4*10^7m
ΔT = change in the temperature of the steel tube = 1°C
α: thermal coefficient expansion of steel = 13*10^-6 /°C
You replace the values of the parameters in the equation (2):
With the new length of the tube, you can calculate the radius of a ring formed with the tube. You again solve the equation (1) for r:
Finally, you compare both r and r' radius:
r' - r = 6,366,280.484m - 6,366,197.724m = 82.76m
Hence, the distance to the ring from the ground is 82.76m
Answer:
<em>The object could fall from six times the original height and still be safe</em>
Explanation:
<u>Free Falling</u>
When an object is released from rest in free air (no friction), the motion is completely dependant on the acceleration of gravity g.
If we drop an object of mass m near the Earth surface from a height h, it has initial mechanical energy of
When the object strikes the ground, all the mechanical energy (only potential energy) becomes into kinetic energy
Where v is the speed just before hitting the ground
If we know the speed v is safe for the integrity of the object, then we can know the height it was dropped from
Solving for h
If the drop had occurred in the Moon, then
Where hM, vM and gM are the corresponding parameters on the Moon. We know v is the safe hitting speed and the gravitational acceleration on the Moon is g_M=1/6 g
This means the object could fall from six times the original height and still be safe