Answer:
In the - j direction, that is negative of the y-axis
Explanation:
As typed in the question, the position of the object is given by the expression in three component ( i, j, k) form:
r (t) = 5 i - (t + 1 ) j + t^3 k
and since the velocity is the derivative of position with respect to time, by doing the derivative of this expression we get:
v(t) = 0 i - 1 j +3 t^2 k
which for the initial velocity requested (that is at time zero) we have:
v(t) = 0 i - 1 j +3 (0)^2 k = = 1 j
Then the direction of the initial velocity is entirely in the direction of the j versor, that is pointing to the negative of the y-axis.
Answer:
v (minimum speed) = 2.90 m/sec.
Maximum value of speed will occur at lowest point of vertical circle.
Explanation:
a) What minimum speed is necessary so that there is no tension in the string at the top of the circle but the rock stays in the same circular path?
Using the force balance expression at the top of the circle,
Gravitational Force + Tension force = Centrifugal force
Given that : T = 0
R = length of string = 0.86 m
mass of the spinning rock = 0.75 kg
v (minimum speed) = 2.90 m/sec.
b) what is the maximum speed the rock can have so that the string does not break?
Here the force balance at bottom of circle is represented by the illustration:
Given that:
maximum tension T = 45 N
maximum speed v = ??
mass m = 0.75 kg
∴
c)
At what point in the vertical circle does this maximum value occur?
Maximum value of speed will occur at lowest point of vertical circle.
This is so because at the lowest point; the tension in string will be maximum.
d. the surface on which the object is moving is made smoother
This is called lubrication, I think ...
b. the weight of the moving object is decreased
If there is less araea of contact because of the weight reduction ("squeezing together") then this could also have an effexct. I thinl though the thrust of the q is on lubrication = oil, talcum powder, thin films of water etc
Please put answers in the comments of actual answers, as I need them! Lots of points! 63 points
Ground water keept the ground at a stable level when it is gone the cavern it was in has no support and is at risk of callaps
Anything less dense than water will float, like oil. Anything more dense than water will sink, like rock.
