Q 10.17: Which of the following statements concerning simple harmonic motion is false? A : A restoring force acts on an object i
1 answer:
Answer:
A : A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement.
Explanation:
Statement A is the false one:
A : A restoring force acts on an object in simple harmonic motion that is directed in the same direction as the object's displacement. --> FALSE. The restoring force in the simple harmonic motion is given by
where
k is the spring constant
x is the displacement of the system, measured with respect to the equilibrium position
As we can notice from the equation, there is a negative sign in front of (kx): this means that the force, F, and the displacement, x, have opposite directions. In fact, the restoring force of a simple harmonic oscillator always acts to restore the equilibrium position, therefore it acts in the opposite direction as that of the displacement.
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Answer:
The net torque is 0.0372 N m.
Explanation:
A rotational body with constant angular acceleration satisfies the kinematic equation:
(1)
with ω the final angular velocity, ωo the initial angular velocity, α the constant angular acceleration and Δθ the angular displacement (the revolutions the sphere does). To find the angular acceleration we solve (1) for α:
Because the sphere stops the final angular velocity is zero, it's important all quantities in the SI so 2.40 rev/s = 15.1 rad/s and 18.2 rev = 114.3 rad, then:
The negative sign indicates the sphere is slowing down as we expected.
Now with the angular acceleration we can use Newton's second law:
(2)
with ∑τ the net torque and I the moment of inertia of the sphere, for a sphere that rotates about an axle through its center its moment of inertia is:
With M the mass of the sphere an R its radius, then:
Then (2) is:
Answer:
<h2>187,500N/m</h2>Explanation:
From the question, the kinectic energy of the train will be equal to the energy stored in the spring.
Kinetic energy = 1/2 mv² and energy stored in a spring E = 1/2 ke².
Equating both we will have;
1/2 mv² = 1/2ke²
mv² = ke²
m is the mass of the train
v is the velocity of then train
k is the spring constant
e is the extension caused by the spring.
Given m = 30000kg, v = 4 m/s, e = 4 - 2.4 = 1.6m
Substituting this values into the formula will give;
30000*4² = k*1.6²
The value of the spring constant is 187,500N/m