Answer:
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg
Explanation:
Hi there!
Due to conservation of energy, the potential energy (PE) of the mass at a height of 3.32 m will be transformed into elastic potential energy (EPE) when it falls on the mattress:
PE = EPE
m · g · h = 1/2 k · x²
Where:
m = mass.
g = acceleration due to gravity.
h = height.
k = spring constant.
x = compression distance
The maximum compression distance is 0.1289 m, then, the maximum elastic potential energy will be the following:
EPE =1/2 k · x²
EPE = 1/2 · 65144 N/m · (0.1289 m)² = 541.2 J
Then, using the equation of gravitational potential energy:
PE = m · g · h = 541.2 J
m = 541.2 J/ g · h
m = 541.2 kg · m²/s² / (9.8 m/s² · 3.32 m)
m = 16.6 kg
The maximum mass that can fall on the mattress without exceeding the maximum compression distance is 16.6 kg.
A machine that provides both constant speed and maximum resistance throughout the full range of motion provides an isokinetic type of muscular contraction. This type of contraction occurs when the muscle would contract and shorten at a consistent and constant speed. To have this contraction, special equipment are to be used. An example of an equipment would be an <span>Isokinetic Dynamometer. </span>However, this type of training is said to be one of the fastest in increasing the muscle strength and the muscle endurance. With this training, the muscles being targeted would gain strength consistently and evenly throughout the whole duration of exercise.
Answer:
106.52 minutes
Explanation:
Given:
Initial distance between Carl and Isaac = 175 miles
speed of Isaac = 65 mph
Speed of Carl = 50 mph
Now, the Carl starts after 35 minutes, but the Isaac has already started so the distance covered by Isaac in 35 minutes will be
=
= 37.91 miles
Therefore,
the distance left between Isaac and Carl = 175 - 37.91 = 137.09 miles
Since Isaac and Carl are moving towards each other,
therefore the relative speed between the both = 65 + 50 = 115 mph
Hence, the time taken to meet =
or
The time taken to meet = 1.192 hours
or
The time taken = 1.192 × 60 = 71.52 minutes
Therefore the total time Isaac have been travelling = 71.52 + 35
= 106.52 minutes
Answer:
The angle between the diagonal and edge = 55 degrees
Explanation:
We will find it by finding the angle between two vectors (a and b)
We will assume it to be a unit cube
Vector a = (1,1,1) (defines the diagonal vector)
Vector b = (1,0,0) (defines the edge vector)
cos (theta) = (a.b)/(|a|*|b|)
theta = 54.74 degrees
theta = 55 degrees (Rounded to the nearest degree)