A cart of mass M is attached to an ideal spring that can stretch and compress equally well. The cart and spring rest on a smooth
horizontal track. The cart is pulled to position A and released. The cart then moves toward position E, where it reverses direction and returns again to position A.
a) show with the sketch of a position diagram how the velocity of the cart changes between the points indicated
b) The dots below represent the cart at different labeled positions. Draw free body diagrams showing and labeling all the forces exerted on the cart at each labeled position. Draw the relative lengths of all vectors to reflect the relative magnitude of all forces. You will create one set of sketches for when the cart is moving to the right and a second set for when the car is moving to the left.
c) do the diagrams above indicate whether the cart is moving left or right? Justify your claim with evidence.
d) at each position, compare the direction of the net force exerted by the spring on the cart and the carts displacement from equilibrium when at that position. Note that this question is not asking whether the cart is moving right or left. Use these results to briefly explain why your claim in part C makes sense.
a) show with the sketch of a position diagram how the velocity of the cart changes between the points indicated
b) The dots below represent the cart at different labeled positions. Draw free body diagrams showing and labeling all the forces exerted on the cart at each labeled position. Draw the relative lengths of all vectors to reflect the relative magnitude of all forces. You will create one set of sketches for when the cart is moving to the right and a second set for when the car is moving to the left.
c) do the diagrams above indicate whether the cart is moving left or right? Justify your claim with evidence.
d) at each position, compare the direction of the net force exerted by the spring on the cart and the carts displacement from equilibrium when at that position. Note that this question is not asking whether the cart is moving right or left. Use these results to briefly explain why your claim in part C makes sense.
1 answer:
It’s important to note that ‘the cart or spring is situated on a frictionless horizontal track’, which means there are no frictional forces acting on them.
Explanation:
a) Per the scenario, when the cart is drawn to position A and then let go, its initial speed at A (at time t=0) is 0 m/s. The cart travels toward position E, reaches a point where it reverses direction, and then heads back to position A. During this second phase, as the cart travels from A to E, its speed increases until it becomes zero again at point E, at which point it changes direction again, thus
( File has been attached)
b) Let’s assume the distance between two successive points is x meters and the spring constant is k N/m
c) ( File has been attached)
d) Moving to the right
e) Moving to the left
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Response: The spring constant is 25 N/m.
Details:
The body’s mass is 25 g, which converts to 0.025 kg (since 1 kg = 1000 g).
The total oscillations are 20 in 4 seconds.
Oscillations per second =
Spring's frequency of vibration is =
The spring constant 'k' can be derived from the relationship involving frequency, mass, and spring constant.
The spring constant is 25 N/m.
1) The wave's period remains constant across different media
2) The wave's velocity varies depending on the medium it travels through
3) As a wave transitions between media, its speed, direction, and wavelength can change, while its frequency stays unchanged
Clarification:
1)
The period of a wave signifies the duration it takes for one full oscillation.
The wave's period is the inverse of its frequency:
where
T denotes the period
f is the frequency
The provided table illustrates that the frequency remains consistent across the three media; hence, the period is unchanged as it solely relies on frequency. We can compute it as we know that
f = 350 Hz
thus the period equals
2)
The velocity of a wave can be derived from the wave equation:
where
f indicates the frequency
is the wavelength
, resulting in a speed of
In the second medium,
, leading to a speed of
In the third medium,
, showing a speed of
As a result, we conclude that the wave's speed varies with the medium.
3)
<pwhen a="" wave="" shifts="" from="" one="" medium="" to="" another="" the="" following="" occurs:="">- The wave's direction alters. Specifically, if the subsequent medium is of greater optical density, the wave bends towards the normal; conversely, it bends away if the second medium is of lesser optical density.
- The wave's speed is affected. The wave decelerates in media with higher optical density and accelerates in those with lower optical density.
- The wave's frequency remains unchanged.
- Ultimately, the wave's wavelength is modified. If moving into a medium of greater optical density, the wavelength decreases, while it increases in one of lower optical density.
Discover more about waves here:
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