Answer:
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A vertical spring with spring constant 23.15 N/m is hanging from a ceiling. A small object is attached to the lower end of the s
1 answer:
Answer:
m= 1.47 kg
Explanation:
Given:
spring constant, K = 23.15 N/m
Displacement, x= 19.79 cm = 0.1979 m
at, x₁= 7.417 cm, v₁= 0.7286 m/s
Now,
x = 19.79 cos ( ωt)
on substituting the values, we get
7.417 x 10⁻² = 19.79 x 10⁻² cos (ωt)
or
cos(ωt) = 0.374
or
ωt = 67.98°
also
v = -0.1979×ωsin (ωt)
also
on substituting the values in the above equation, we get
0.7286 = -0.1979 sin ( 67.98°)
3.68 =-(0.927)
or
T = 1.582 sec
also,
where, m is the mass
on substituting the values, we have
on squaring both sides and solving, we have
m= 1.47 kg
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Answer:
Explanation:
For an object to move with constant velocity, the acceleration of the object must be zero:
.
As the net force equals acceleration multiplied by mass , this must mean:
.
So, the sum of the three forces must be zero:
,
this implies:
.
To obtain this sum, its easier to work in Cartesian representation.
First we need to define an Frame of reference. Lets put the x axis unit vector pointing east, with the y axis unit vector
pointing south, so the positive angle is south of east. For this, we got for the first force:
,
as is pointing north, and for the second force:
,
as is pointing west.
Now, our third force will be:
But, we need the magnitude and the direction.
To find the magnitude, we can use the Pythagorean theorem.
this is the magnitude.
To find the direction, we can use:
and this is the angle south of east.