Answer:
Explanation:
Given that,
The spring constant of spring 1,
The motion of the object on spring 1 has twice the amplitude as the motion of the object on spring 2,
As the magnitude of the maximum velocity is the same in each case, it means the maximum kinetic energy is same in each case. In other words, the total energy is same.
So, the spring constant of spring 2 is 920 N/m. Hence, this is the required solution.
Answer:
R=9.
C=(2,-2,0).
Explanation:
Lets try to find how can be written in the form of
, since then its radius R and center of coordinates C=(a,b,c) would be easily recognizable.
Since we have the terms -4x and +4y, they seem to have come from the terms and
, and we would need to take care of the extra +4 by substracting then. More explicitly:
, as we had originally with the x terms
, as we had originally with the y terms
Which means:
Or, putting all together:
So our radius is 9 and the center is (2,-2,0).
d.Both points have the same instantaneous angular velocity.
Explanation:
Let's analyze each option one by one:
a.the angular velocity at point A is greater than that of point B. --> FALSE. In fact, for a rigid body (such as the rigid wheel in this problem), all the points along the body rotates with the same angular velocity. This is because the angular velocity is defined as
where is the angular displacement and t is the time taken. Therefore, all the points rotate by the same angle
in the same time t.
b.Both points have the same centripetal acceleration. --> FALSE. The centripetal acceleration of a point along the disk is given by
where is the angular velocity and r is the distance of the point from the axis of rotation. Here A is located farther away from the axis with respect to B, so it will have a greater centripetal acceleration.
c.Both points have the same tangential acceleration. --> FALSE. The tangential acceleration is given by
where is the angular acceleration.
is the same for every point for a rigid body, but
is not (A is located farther away), so A and B do not have same tangential acceleration.
d.Both points have the same instantaneous angular velocity. --> TRUE. This is true for what we said at point A).
e.Each second, point A turns through a greater angle than point B. --> FALSE. The two points cover the same angular displacement in the same time, since they have same angular velocity.
Learn more about circular motion:
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