Note: I'm not sure what do you mean by "weight 0.05 kg/L". I assume it means the mass per unit of length, so it should be "0.05 kg/m".
Solution:
The fundamental frequency in a standing wave is given by
where L is the length of the string, T the tension and m its mass. If we plug the data of the problem into the equation, we find
The wavelength of the standing wave is instead twice the length of the string:
So the speed of the wave is
And the time the pulse takes to reach the shop is the distance covered divided by the speed:
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Given :
The ball of a ballpoint pen is 0.5 mm in diameter and has an ASTM grain size of 12.
To Find :
How many grains are there in the ball?
Solution :
Volume of ball of the ballpoint is :
Now, grain size of 12 has about 520000 grains/mm³.
Therefore, number of grains are :
Here in order to find out the distance between two planes after 3 hours can be calculated by the concept of relative velocity
here
speed of first plane is 700 mi/h at 31.3 degree
speed of second plane is 570 mi/h at 134 degree
now the relative velocity is given as
now the distance between them is given as
so the magnitude of the distance is given as
miles
so the distance between them is 2985.6 miles
Answer:
Approximately , assuming friction between the vehicle and the ground is negligible.
Explanation:
Let denote the mass of the vehicle. Let denote the initial velocity of the vehicle. Let denote the spring constant (needs to be found.) Let denote the maximum displacement of the spring.
Convert velocity of the vehicle to standard units (meters per second):
.
Initial kinetic energy () of the vehicle:
.
When the vehicle is brought to a rest, the elastic potential energy () stored in the spring would be:
.
By the conservation of energy, if the friction between the vehicle and the ground is negligible, the initial of the vehicle should be equal to the of the vehicle. In other words:
.
Rearrange this equation to find an expression for , the spring constant:
.
Substitute in the given values , , and :