Answer:
k = 6,547 N / m
Explanation:
This laboratory experiment is a simple harmonic motion experiment, where the angular velocity of the oscillation is
w = √ (k / m)
angular velocity and rel period are related
w = 2π / T
substitution
T = 2π √(m / K)
in Experimental measurements give us the following data
m (g) A (cm) t (s) T (s)
100 6.5 7.8 0.78
150 5.5 9.8 0.98
200 6.0 10.9 1.09
250 3.5 12.4 1.24
we look for the period that is the time it takes to give a series of oscillations, the results are in the last column
T = t / 10
To find the spring constant we linearize the equation
T² = (4π²/K) m
therefore we see that if we make a graph of T² against the mass, we obtain a line, whose slope is
m ’= 4π² / k
where m’ is the slope
k = 4π² / m'
the equation of the line of the attached graph is
T² = 0.00603 m + 0.0183
therefore the slope
m ’= 0.00603 s²/g
we calculate
k = 4 π² / 0.00603
k = 6547 g / s²
we reduce the mass to the SI system
k = 6547 g / s² (1kg / 1000 g)
k = 6,547 kg / s² =
k = 6,547 N / m
let's reduce the uniqueness
[N / m] = [(kg m / s²) m] = [kg / s²]
Answer:
Maximum height reached = 39.39 m
Explanation:
At maximum height
We have equation of motion v² = u² + 2as
Consider the vertical motion of baseball,
Initial velocity, u = 32.1sin60=27.8 m/s
Final velocity, v = 0 m/s
Acceleration, a = -9.81 m/s²
Substituting
v² = u² + 2as
0 = 27.8² + 2 x (-9.81) x s
s = 39.39 m
Maximum height reached = 39.39 m
The upward force exerted on the board by the support is mathematically given as
Fu= 764.8 N
<h3>What is the upward force exerted on the board by the support?</h3>
Generally, the equation for is mathematically given as
Considering that the Net Force on the system is null
The weight of the children plus the weight of the board equals the upward force imposed on the support.
The upward force
Fu= 440 + 272 + 52.8 N
Fu= 764.8 N
In conclusion, he upward force exerted on the board by the support
Fu= 764.8 N
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