Picture of sinusoidal curve with 5 points

In summary: C) False -- not sure, The Attempt at a SolutionA) Greater than -- down direction is positive and acceleration is gravityB) True -- velocity is slope=0, therefore acceleration=0C) False -- not sure, D) Less than -- but not sure, speed is magnitude of velocity components, and there is no vertical component of velocity at D, so it should be less than the speed at B.E) Equal to -- no acceleration in x-direction, unless there's not constant speed..F) Equal to -- not sure, there is no vertical component of velocity here
  • #1
NAkid
70
0

Homework Statement


Sorry I can't provide a visual for this problem, but I'll try my best to explain it
Given: picture of sinusoidal curve with 5 points from left to right, H C D B A
H is on downward slope
C is a min
D is a max
B is on upward slope
A is on upward slope to the right of B

The bead slides starting from rest at position H on the frictionless wire. The direction of the gravitational field is in the -y direction (toward the bottom of the page).
(Select T-True, F-False, G-Greater than, L-Less than, E-Equal to. If the first is T, the second G, and the rest F, enter
TGFFFF).

A) The acceleration in the y-direction at C is ... zero.
B) The acceleration at D is zero.
C) The velocity at B equals the velocity at D.
D) The speed at D is ... the speed at B.
E) The acceleration in the x-direction at C is ... zero.
F) The speed at C is ... the speed at D.


The Attempt at a Solution



A) Greater than -- down direction is positive and acceleration is gravity
B) True -- velocity is slope=0, therefore acceleration=0
C) False -- not sure,
D) Less than -- but not sure, speed is magnitude of velocity components, and there is no vertical component of velocity at D, so it should be less than the speed at B
E) Equal to -- no acceleration in x-direction, unless there's not constant speed..
F) Equal to -- not sure, there is no vertical component of velocity here
 
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  • #2
NAkid said:
A) Greater than -- down direction is positive and acceleration is gravity

Your answer is correct, but not your reasoning. The up direction is positive, and
gravity is not the only source of acceleration.

B) True -- velocity is slope=0, therefore acceleration=0
If the velocity in the y direction is 0, it doesn't follow that the acceleration in the y direction is 0.

There is however the problem that the bead never arrives at D. The bead starts out with 0 velocity in a position lower than D. So it has to gain potential energy to get to D, but it starts out with no kinetic energy, so there's no way it can gain this potential energy.
This means I can't answer B, C, D and F

E is correct
 
  • #3
it's actually not a perfect sinusoidal curve; D is a relative max I should have said -- H is above it
 
  • #4
In that case B is False. The acceleration has 2 components, one along the wire and one perpendicular. The perpendicular component is only 0 for a straight piece of wire.

For C both the magnitude and direction of the velocity must be the same. the direction of the bead is in the direction of the wire

D and F: use conservation of energy. If the bead is lower it has less potential energy ...
 

Related to Picture of sinusoidal curve with 5 points

1. What is a sinusoidal curve?

A sinusoidal curve is a graphical representation of a sine or cosine function. It is a smooth, repetitive wave-like curve that occurs in many natural phenomena, such as sound waves and electromagnetic radiation.

2. How many points are needed to draw a sinusoidal curve?

At least two points are needed to draw a sinusoidal curve. These points should be located on different cycles of the curve to accurately represent its shape.

3. What is the significance of 5 points on a sinusoidal curve?

Five points on a sinusoidal curve can represent important characteristics of the curve, such as the amplitude, period, and phase shift. These points can also be used to calculate the equation of the curve.

4. How can a sinusoidal curve be used in real-life applications?

Sinusoidal curves are commonly used in fields such as engineering, physics, and mathematics to model and analyze various phenomena, such as sound, light, and electrical signals. They are also used in fields such as finance and economics to study periodic trends and fluctuations.

5. How can I determine the equation of a sinusoidal curve with 5 points?

To determine the equation of a sinusoidal curve, you can use the five points to find the values of the amplitude, period, and phase shift, and then plug these values into the general form of the sine or cosine function. Alternatively, you can use regression analysis or other mathematical methods to find the equation that best fits the given data points.

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