A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4 sin 4t lb. If the mass is pulled down 6 in. and then released, determine the position of the mass at any time. Determine the first four times at which the velocity of the mass is zero
Answers
Answer:
Explanation:
The equation of force is
F = 4 sin 4 t
Compare with the standard equation
f = A sin wt
where, w is the angular frequency and A is the amplitude.
Now
w = 4 rad/s
Let the time period is T.
the relation for the time period is
the time period is defined as the time taken by the body to complete one oscillation.
So, the velocity is zero at the extreme points where the object is at time, T/4 and its odd T/2, 3T/4, 3T/2, etc.
So, the velocity is zero at time
Final answer:
To determine the position of the mass and the times when the velocity is zero in a mass-spring system.
Explanation:
To determine the position of the mass at any time, we need to solve the equation of motion for the mass-spring system. The equation is:
mx'' + kx = Fext
where m is the mass, x is the displacement of the mass from its equilibrium position, k is the spring constant, and Fext is the external force. We can solve this differential equation to find the position of the mass as a function of time.
To determine the first four times at which the velocity of the mass is zero, we need to solve for the velocity of the mass, which is given by:
v = x'
We can find the times at which the velocity is zero by finding the values of t for which x' = 0.
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Related Questions
Two objects with different masses collide and bounce back after an elastic collision. Before the collision, thetwo objects were moving at velocities equal in magnitude but opposite in direction. After the collision, A. the less massive object had gained momentum. B. the more massive object had gained momentum. C. both objects had the same momentum. D. both objects lost momentum.
The (nonconservative) force propelling a 1.50 103-kg car up a mountain road does 5.00 106 J of work on the car. The car starts from rest at sea level and has a speed of 25.0 m/s at an altitude of 1.90 102 m above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are non conservative forces.
The index of refraction for red light in material X is measured at 1.80. Blue light travels 5 × 10⁶ m/s slower than red light in this material. What is the index of refraction for blue light in material X?
Which of the following is a true statement? A) It's easier to lift a heavy weight straight up than to slide it up a ramp. B) When you use a lot of effort, a load becomes lighter. C) When you use a minimum amount of effort, a load becomes heavier. D) When you increase the distance over which effort is expended, you don't have to work as hard.
A. x>0 but xB. x=A
C. x<0.
D. x=0.
E. None of the above
Answers
Answer:
The correct answer is option E. This is because when a body is undergoing simple harmonic motion, the displacement, velocity and acceleration are constantly changing with respect to position and time.
Explanation:
When the body is passing through the equilibrium position so that the displacement at that point is zero, the velocity at that point is either maximum or minimum (Vmax or Vmin) which is dependent on which way the body is moving (the chosen direction of positive sense of motion). At the equilibrium position the acceleration is zero because the net force acting on the body is zero (that is the sun of the forces acting on the body along both directions of motion is equal to zero). Also when the body is at either its maximum positive displacemt, x = +A, or its maximum negative displacement x = -A, the velocity is zero and the body is instantaneously at rest. At this points the force (in either direction) acting on the body has it maximum value and as a result the acceleration has it maximum magnitude whether negative or positive depending on the chosen direction positive sense of motion.
At any other point in the course of the SHM (simple harmonic motion), the velocity (V) and acceleration (a) of the always have nonzero values and as a result they are never simultaneously equal to zero.
Thank you very much reading and I hope this is helpful to you.
Answers
Property Electromagnet Magnet
Permanent magnet X
Temporary magnet X X
Magnetic field created by aligning domains X
Moving electric charge produces magnetic field X
B.
Property Electromagnet Magnet
Permanent magnet X
Temporary magnet X X
Magnetic field created by aligning domains X
Moving electric charge produces magnetic field X
C.
Property Electromagnet Magnet
Permanent magnet X
Temporary magnet X X
Magnetic field created by aligning domains X
Moving electric charge produces magnetic field X
D.
Property Electromagnet Magnet
Permanent magnet X
Temporary magnet X X
Magnetic field created by aligning domains X
Moving electric charge produces magnetic field X
Answers
B.
Property Electromagnet Magnet
Permanent magnet X
Temporary magnet X X
Magnetic field created by aligning domains X
Moving electric charge produces magnetic field X
both took 4 hours to complete their walk. Their routes are shown.
Route in miles
D2 E
End
B2C
li
F
2
LL
3
10
Start
G
A
Which statement is true about Debby and Ben's average speed?
Debby's average speed was twice Ben's average speed,
Ben and Debby's average speed was the same,
Debby's average speed was three times Ben's average speed,
Ben's average speed was twice Debby's average speed.
Answers
Answers
Answer:
Satellites are placed into orbit at least 150km above Earth's surface to ensure that they remain above the atmosphere.
The velocity required to keep a balance between the inertia of the motion of the satellite and the earth's gravitational pull, which is called the orbital velocity, essentially depends on its distance above the surface of the Earth. The higher this distance, the longer the satellite will stay in the orbit. Otherwise it might run into the atmosphere and could get burnt up there.
Answers
On Earth: g = 9.81 m/s²
m = 20 kg
W = m · g = 20 kg · 9.81 m/s² = 196.2 N