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:
We have to remember a point , which is ' the cart or spring rest on a smooth horizontal track ' , i.e., any frictional force doesn't take place.
<u>Explanation:</u>
a) According to the question the cart is pulled to position A and released, i.e., the velocity of the cart at A initially (say time,t=0) is 0 m/s ,then moves toward position E, where it reverses direction and returns again to position A , in the 2nd phase cart moves along A to E , the cart's velocity increase and again goes to zero at point E and again change the direction, hence
( File has been attached)
b) Let's , the distance between two consecutive points is x meter and the spring constant is k N.m
c) ( File has been attached)
d) Movinf Right
e) Moving left
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a) Electric field inside the paint layer: zero
b) Electric field just outside the paint layer:
c) Electric field 8.00 cm outside the paint layer:
Explanation:
a)
We can find the electric field inside the paint layer by applying Gauss Law: the total flux of the electric field through a gaussian surface is equal to the charge contained within the surface divided by the vacuum permittivity, mathematically:
where
E is the electric field
dS is the element of surface
q is the charge within the gaussian surface
is the vacuum permittivity
Here we want to find the electric field just inside the paint layer, so we take a sphere of radius as Gaussian surface, where
R = 6.5 cm = 0.065 m is the radius of the plastic sphere (half the diameter)
By taking the sphere of radius r, we note that the net charge inside this sphere is zero, therefore
So we have
which means that the electric field inside the paint layer is zero.
b)
Now we want to find the electric field just outside the paint layer: therefore, we take a Gaussian sphere of radius
The area of the surface is
And since the electric field is perpendicular to the surface at any point, Gauss Law becomes
The charge included within the sphere in this case is the charge on the paint layer, therefore
So, the electric field is:
where the negative sign means the direction of the field is inward, since the charge is negative.
c)
Here we want to calculate the electric field 8.00 cm outside the surface of the paint layer.
Therefore, we have to take a Gaussian sphere of radius:
Gauss theorem this time becomes
And the charge included within the sphere is again the charge on the paint layer,
Therefore, the electric field is
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