1. The correct answer among the choices provided is the third option. Measuring the temperature increase of water from doing work by stirring it is an experiment generally regarded as being first carried out by James Joule.
2. Joule's experiment directly shows that heat is a form of energy. He wanted to make a different way of measuring energy.
a. The disk starts at rest, so its angular displacement at time
is

It rotates 44.5 rad in this time, so we have

b. Since acceleration is constant, the average angular velocity is

where
is the angular velocity achieved after 6.00 s. The velocity of the disk at time
is

so we have

making the average velocity

Another way to find the average velocity is to compute it directly via

c. We already found this using the first method in part (b),

d. We already know

so this is just a matter of plugging in
. We get

Or to make things slightly more interesting, we could have taken the end of the first 6.00 s interval to be the start of the next 6.00 s interval, so that

Then for
we would get the same
.
Answer:
H = 1/2 g t^2 where t is time to fall a height H
H = 1/8 g T^2 where T is total time in air (2 t = T)
R = V T cos θ horizontal range
3/4 g T^2 = V T cos θ 6 H = R given in problem
cos θ = 3 g T / (4 V) (I)
Now t = V sin θ / g time for projectile to fall from max height
T = 2 V sin θ / g
T / V = 2 sin θ / g
cos θ = 3 g / 4 (T / V) from (I)
cos θ = 3 g / 4 * 2 sin V / g = 6 / 4 sin θ
tan θ = 2/3
θ = 33.7 deg
As a check- let V = 100 m/s
Vx = 100 cos 33.7 = 83,2
Vy = 100 sin 33,7 = 55.5
T = 2 * 55.5 / 9.8 = 11.3 sec
H = 1/2 * 9.8 * (11.3 / 2)^2 = 156
R = 83.2 * 11.3 = 932
R / H = 932 / 156 = 5.97 6 within rounding
Answer:

Explanation:
given,
F = 14.1 i + 0 j + 5.1 k
displacement = 6 m
Assuming block is moving in x- direction
we know,
dW = F dx


![W = F[x]_0^6](https://tex.z-dn.net/?f=W%20%3D%20F%5Bx%5D_0%5E6)


hence, work done by the force is equal to 
Answer:
Explanation:
Kinetic Energy formula:
KE =
mv²
m=mass
v=speed
Given:
m=0.25kg
v=2.5m/s
Plug the values in:
KE = 1/2(0.25kg)(2.5m/s)²
KE = 0.78125 J (Joules)