A mass m on a spring with a spring constant k is in simple harmonic motion with a period T. If the same mass is hung from a spri
1 answer:
Answer:
d) decreased by a factor of the square root of 3
Explanation:
Data provided in the question
Mass = M on a spring
Spring constant = k
Period = T
Spring constant = 3k in the case when the same mass is hung
Based on the above information, the period of the motion is
As we know that
Based on this, there is a decrease by a factor of the square root of 3
hence, the correct option is d.
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Answer:
The magnitude and direction of the force applied by Steinberg are approximately 15.192 newtons and 126.704º.
Explanation:
The chew toy is at equilibrium and experimenting three forces from three distinct dogs. The Free Body Diagram depicting the system is attached below. By Newton's Laws we construct the following equations of equilibrium: (<em>Sp</em> is for Spot, <em>F</em> is for Fido and <em>St</em> is for Steinberg) All forces and angles are measured in newtons and sexagesimal degrees, respectively:
(1)
(2)
If we know that ,
and
, then the components of the force done by Steinberg on the chewing toy is:
The magnitud of the force is determined by Pythagorean Theorem:
Since the direction of this force is in the 3rd Quadrant on Cartesian plane, we determine the direction of the force with respect to the eastern semiaxis:
The magnitude and direction of the force applied by Steinberg are approximately 15.192 newtons and 126.704º.
Answer:
θ = 12.95º
Explanation:
For this exercise it is best to separate the process into two parts, one where they collide and another where the system moves altar the maximum height
Let's start by finding the speed of the bar plus clay ball system, using amount of momentum
The mass of the bar (M = 0.080 kg) and the mass of the clay ball (m = 0.015 kg) with speed (v₀ = 2.0 m / s)
Initial before the crash
p₀ = m v₀
Final after the crash before starting the movement
= (m + M) v
p₀ =
m v₀ = (m + M) v
v = v₀ m / (m + M)
v = 2.0 0.015 / (0.015 +0.080)
v = 0.316 m / s
With this speed the clay plus bar system comes out, let's use the concept of conservation of mechanical energy
Lower
Em₀ = K = ½ (m + M) v²
Higher
= U = (m + M) g y
Em₀ =
½ (m + M) v² = (m + M) g y
y = ½ v² / g
y = ½ 0.316² / 9.8
y = 0.00509 m
Let's look for the angle the height from the pivot point is
L = 0.40 / 2 = 0.20 cm
The distance that went up is
y = L - L cos θ
cos θ = (L-y) / L
θ = cos⁻¹ (L-y) / L
θ = cos⁻¹-1 ((0.20 - 0.00509) /0.20)
θ = 12.95º