Answer:
a. 3.07 b. 1.26
Explanation:
Given that A = -3.07i + 3.17j and B = b1i + b1j and C = A + B = 0i + 4.43j
Since A + B = -3.07i + 3.17j + b1i + b2j
= (-3.07 + b1)i + (3.17 + b2)j
So,(-3.07 + b1)i + (3.17 + b2)j = 0i + 4.43j
Comparing components,
-3.07 + b1 = 0 (1) and 3.17 + b2 = 4.43 (2)
a. From (1), b1 = 3.07
b. From(2) b2 = 4.43 - 3.17 = 1.26
Answer:
faster; more kinetic energy
Explanation:
Answer:
A: The acceleration is 7.7 m/s up the inclined plane.
B: It will take the block 0.36 seconds to move 0.5 meters up along the inclined plane
Explanation:
Let us work with variables and set

As shown in the attached free body diagram, we choose our coordinates such that the x-axis is parallel to the inclined plane and the y-axis is perpendicular. We do this because it greatly simplifies our calculations.
Part A:
From the free body diagram we see that the total force along the x-axis is:

Now the force of friction is
where
is the normal force and from the diagram it is 
Thus
Therefore,

Substituting the value for
we get:

Now acceleration is simply

The negative sign indicates that the acceleration is directed up the incline.
Part B:

Which can be rearranged to solve for t:

Substitute the value of
and
and we get:
which is our answer.
Notice that in using the formula to calculate time we used the positive value of
, because for this formula absolute value is needed.
Answer:
The answer to the question is;
The total potential energy of the mass on the spring when the mass is at either endpoint of its motion is 5.0255 Joules.
Explanation:
To answer the question, we note that the maximum speed is 2.30 m/s and the mass is 1.90 kg
Therefore the maximum kinetic energy of motion is given by
Kinetic Energy, KE =
Where,
m = Attached vibrating mass = 1.90 kg
v = velocity of the string = 2.3 m/s
Therefore Kinetic Energy, KE =
×1.9×2.3² = 5.0255 J
From the law of conservation of energy, we have the kinetic energy, during the cause of the vibration is converted to potential energy when the mass is at either endpoint of its motion
Therefore Potential Energy PE at end point = Kinetic Energy, KE at the middle of the motion
That is the total potential energy of the mass on the spring when the mass is at either endpoint of its motion is equal to the maximum kinetic energy.
Total PE = Maximum KE = 5.0255 J.