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Alina [70]
3 years ago
11

A mass is undergoing simple harmonic motion. When its displacement is 0, it is at its equilibrium position. At that moment, its

speed is _______ and its acceleration is _______.
0, 0
max, max
0, max
max, o
Physics
1 answer:
Nostrana [21]3 years ago
4 0

Answer:

Its speed is maximum and its acceleration is zero

Explanation:

- Concerning the speed:

In a simple harmonic motion, the speed can be determined through the law of conservation of energy. In fact, we have that the total mechanical energy of the system, which is sum of elastic potential energy U and kinetic energy K, is constant:

E=U+K=\frac{1}{2}kx^2+\frac{1}{2}mv^2

where k is the spring constant, x is the displacement, m is the mass and v is the speed.

We see that when the displacement is 0, x = 0: this means that the elastic potential energy U is also 0, therefore the kinetic energy K is maximum, and so the speed v is also maximum.

- Concerning the acceleration:

According to Newton's second law, the acceleration of the system is proportional to the net force:

a=\frac{F}{m}

the net force is just the restoring force of the spring, given by Hooke's law:

F=-kx

So, the acceleration is

a=-\frac{kx}{m}

and we see that when the displacement is zero, x = 0, and so the acceleration is also zero.

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A thin rod of length 0.75 m and mass 0.42 kg is suspended
MrRissso [65]

Answer:

a)  K = 0.63 J, b)  h = 0.153 m

Explanation:

a) In this exercise we have a physical pendulum since the rod is a material object, the angular velocity is

         w² = \frac{m g d}{I}

where d is the distance from the pivot point to the center of mass and I is the moment of inertia.

The rod is a homogeneous body so its center of mass is at the geometric center of the rod.

              d = L / 2

the moment of inertia of the rod is the moment of a rod supported at one end

              I = ⅓ m L²

we substitute

            w = \sqrt{\frac{mgL}{2}  \ \frac{1}{\frac{1}{3} mL^2} }

            w = \sqrt{\frac{3}{2}  \ \frac{g}{L} }

            w = \sqrt{ \frac{3}{2} \ \frac{9.8}{0.75}  }

            w = 4.427 rad / s

an oscillatory system is described by the expression

              θ = θ₀ cos (wt + Φ)

the angular velocity is

             w = dθ /dt

             w = - θ₀ w sin (wt + Ф)

In this exercise, the kinetic energy is requested in the lowest position, in this position the energy is maximum. For this expression to be maximum, the sine function must be equal to ±1

In the exercise it is indicated that at the lowest point the angular velocity is

           w = 4.0 rad / s

the kinetic energy is

           K = ½ I w²

           K = ½ (⅓ m L²) w²

           K = 1/6 m L² w²

           K = 1/6 0.42 0.75² 4.0²

           K = 0.63 J

b) for this part let's use conservation of energy

starting point. Lowest point

             Em₀ = K = ½ I w²

final point. Highest point

             Em_f = U = m g h

energy is conserved

             Em₀ = Em_f

             ½ I w² = m g h

             ½ (⅓ m L²) w² = m g h

             h = 1/6 L² w² / g

             h = 1/6 0.75² 4.0² / 9.8

             h = 0.153 m

5 0
2 years ago
What is the final velocity of a car that starts at 22 m/s and accelerates at 3.78 m/s for distance of 45 m
Pepsi [2]

v^2 = v0^2 +2ad v^2 = 22^2 + 2*3.78*45 = 824.2 v= √824.2 = 28.7 m/s

5 0
3 years ago
Which statement is true according to Newton's first law of motion?
katrin2010 [14]
C) In the absence of an unbalanced force, an object at rest will stay at rest and an object in motion will stay in motion.

hope this helps and have a great day :)







8 0
3 years ago
Read 2 more answers
A sailboat moves north for a distance of 10.00 km when blown by a wind from the exact south with a force of 5.00 x 10^4 n. how m
Nataliya [291]
Work is defined as the force times the distance which is mathematically expressed W = Fxd. The given force is 5x10^4 and the distance is 10000 m (the distance is converted as meter because Nm = J) the work done by the wind is W = 5x10^4 N (10000) = 500 x 10^6 Joules. I hope it answered your question
8 0
3 years ago
Two families meet at the park at 10:00am. Each family uses a different way of transportation to get there. The Gonzalez family l
pav-90 [236]

Firstly, we need to make the times and distance equal to compare.

1hr=60mins
Gonz drove 90km in 60mins,so they would drive 45km in 30 mins dividing it by 2.
Because the Rivs had gone 30km in 30mins, Gonz were faster.

For the adverage speed, we should first add the speed of each family in mph , so 90+60, which equals 150 and divide that by 2 because there are 2 speeds so the average speed is 75mph.

P.S English is my second language so tell me if you don't understand something and I will try and explain.
5 0
3 years ago
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