Answer:
0.005 m
Explanation:
length of steel (L°) = 12 m
initial temperature (T) = 16 degrees
expected temperature (T') = 50 degrees
We can find how large the gaps should be if the track is not to buckle when the temperature is as high as 50 degrees from the formula below
ΔL = ∝L°ΔT where
ΔL = x 12 x (50-16) = 0.005 m
The mass attached to the spring must be 0.72 kg
Explanation:
The frequency of vibration of a spring-mass system is given by:
(1)
where
k is the spring constant
m is the mass attached to the spring
We can find the spring constant by using Hookes' law:
where
F is the force applied on the spring
x is the stretching of the spring
When a mass of m = 2.82 kg is applied to the spring, the force applied is the weight of the mass, so we have
and using and
, we find
Now we want the frequency of vibration to be
f = 7.42 Hz
So we can rearrange eq.(1) to find the mass m that we need to attach to the spring:
#LearnwithBrainly
Answer:
- 1.07 ft
Explanation:
V1 = (-5, 7, 2)
V2 = (3, 1, 2)
Projection of v1 along v2, we use the following formula
=\frac{\overrightarrow{V1}.\overrightarrow{V2}}{V2}
So, the dot product of V1 and V2 is = - 5 (3) + 7 (1) + 2 (2) = -15 + 7 + 4 = -4
The magnitude of vector V2 is given by
=
So, the projection of V1 along V2 = - 4 / 3.74 = - 1.07 ft
Thus, the projection of V1 along V2 is - 1.07 ft.
so we need to find the direction of v2