You can tell a lot about an object that's not moving,
and also a lot about the forces acting on it:
==> If the box is at rest on the table, then it is not accelerating.
==> Since it is not accelerating, I can say that the forces on it are balanced.
==> That means that the sum of all forces acting on the box is zero,
and the effect of all the forces acting on it is the same as if there were
no forces acting on it at all.
==> This in turn means that all of the horizontal forces are balanced,
AND all of the vertical forces are balanced.
Horizontal forces:
sliding friction, somebody pushing the box
All of the forces on this list must add up to zero. So ...
(sliding friction force) = (pushing force), in the opposite direction.
If nobody pushing the box, then sliding friction force = zero.
Vertical forces:
gravitational force (weight of the box, pulling it down)
normal force (table pushing the box up)
All of the forces on this list must add up to zero, so ...
(Gravitational force down) + (normal force up) = zero
(Gravitational force down) = -(normal force up) .
Complete question is;
The abc battery company claims that their batteries last 100 hours, on average. You decide to conduct a test to see if the company's claim is true. You believe that the mean life may be different from the 100 hours the company claims. you decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. some of the information related to the hypothesis test is presented below:
Test of H0: μ = 100 versus H1: μ ≠ 100
Sample mean: 98.5
Std error of mean: 0.777
Assuming the life length of batteries is normally distributed, what is the p-value associated with this test?
Answer:
p-value = 0.00001
Explanation:
We are given;
Null hypothesis; H0: μ = 100
Alternative Hypothesis; H1: μ ≠ 100
Sample mean: x = 98.5
Standard error of mean; s = 0.777
To find the test statistic, we will use the formula;
t = (x - μ)/(s/√n)
t = (98.5 - 100)/(0.777/√20)
t = -1.5/0.1737
t = -8.64
Now, from online p-value from t-score calculator attached, using t = -8.64; DF = n - 1 = 20 - 1 = 19; two tail distribution;significance level of 0.05; we have;
The p-value = 0.00001
Answer:
Explanation:
Given:
- Three identical charges q.
- Two charges on x - axis separated by distance a about origin
- One on y-axis
- All three charges are vertices
Find:
- Find an expression for the electric field at points on the y-axis above the uppermost charge.
- Show that the working reduces to point charge when y >> a.
Solution
- Take a variable distance y above the top most charge.
- Then compute the distance from charges on the axis to the variable distance y:
- Then compute the angle that Force makes with the y axis:
cos(Q) = sqrt(3)*a / 2*r
- The net force due to two charges on x-axis, the vertical components from these two charges are same and directed above:
F_1,2 = 2*F_x*cos(Q)
- The total net force would be:
F_net = F_1,2 + kq / y^2
- Hence,
- Now for the limit y >>a:
- Insert limit i.e a/y = 0
Hence the Electric Field is off a point charge of magnitude 3q.
On a velocity - time graph, if the line crosses the x - axis it depicts that the object has started moving in the opposite direction.
Explanation :
The heating curve shows how water changes from one state of matter to another based on temperature and the addition or removal of heat over time.
Initially, ice is heated until its temperature reaches and changes to liquid state.
From the attached graph it is clear that until the temperature will rise steadily. Here, the liquid begins to vaporize. Vaporization is the state of matter at which liquid state changes to the gaseous state.
So, E is the point which shows the gaseous state.