Newton's second law of motion can be formally stated as follows: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Answer:
spring constant of the spring is 1820.44 N/m
Explanation:
given data
ball mass = 4 kg
speed = 16 m/s
distance = 0.75 m
to find out
spring constant of the spring
solution
we know that kinetic energy of ball = energy store in spring as compression
so we can express it as
0.5 × m × v² = 0.5 × k × x² ....................1
so put here value we get spring constant k
m × v² = k × x²
4 × 16² = k × 0.75²
solve it we get
k = 1820.44 N/m
so spring constant of the spring is 1820.44 N/m
Answer:
91.48N/m
Explanation:
In a spring-mass system undergoing a simple harmonic motion, the inverse of the frequency f, of oscillation is proportional to the square root of the mass m, and inversely proportional to the square root of the spring constant, k. This can be expressed mathematically as follows;
=
-----------(i)
From the question;
f = 3.26 Hz
m = 0.218kg
Substitute these values into equation (i) as follows;
=
[<em>Square both sides</em>]
(
)² = (
)²(
)
(
) =
²(
) [<em>Take </em>
<em> to be 3.142</em>]
(
) =
²(
)
(
) =
(
)
(
) = (
) [<em>Switch sides</em>]
(
) = (
) [<em>Re-arrange</em>]
(
) = (
) [<em>Cross-multiply</em>]
k = 8.608 x 10.6276
k = 91.48N/m
Therefore, the spring constant of the spring is 91.48N/m
Answer:
6.25 m/s
196 kg/s
Explanation:
The areas of the pipe from big to small:


As the product of speed and cross-section area is constant, the speed in the smaller pipe would be


The mass flow rate would be:
