Answer:
Explanation:
A Spring stretches / compresses when force is applied on them and they are governed by the Hookes Law which states that the force required to stretch or compress a spring is directly proportional to the distance it is stretched.

F is the force applied and x is the elongation of the spring
k is the spring constant.
negative sign indicates the change in direction from equilibrium position.
In the given question, we dont have force but we know that the pan is hanging. We also know from the Newton's second law of motion that

Inserting this into Hooke's Law

computing it for x,

This is the model which will tell the length of the spring against change in the mass located in the pan.
The work done will be equal to the potential energy of the piano at the final position
P.E=m.g.h
.consider the plank the hypotenuse of the right triangle formed with the ground
.let x be the angle with the ground=31.6°
.h be the side opposite to the angle x (h is the final height of the piano)
.let L be the length of the plank
sinx=opposite side / hypotenuse
= h/L
then h=L.sinx=3.49×sin31.6°=0.638m
weight w=m.g
m=w/g=3858/10=385.8kg
Consider Gravity g=10m/s2
then P.E.=m.g.h=385.8kg×10×0.638=2461.404J
then Work W=P.E.=2451.404J
Answer
given,
v = 128 ft/s
angle made with horizontal = 30°
now,
horizontal component of velocity
vx = v cos θ = 128 x cos 30° = 110.85 ft/s
vertical component of velocity
vy = v sin θ = 128 x sin 30° = 64 m/s
time taken to strike the ground
using equation of motion
v = u + at
0 =-64 -32 x t
t = 2 s
total time of flight is equal to
T = 2 t = 2 x 2 = 4 s
b) maximum height
using equation of motion
v² = u² + 2 a h
0 = 64² - 2 x 32 x h
64 h = 64²
h = 64 ft
c) range
R = v_x × time of flight
R = 110.85 × 4
R = 443.4 ft
<u>Answer:</u> The final temperature of the solution is 
<u>Explanation:</u>
The amount of heat released by coffee will be absorbed by aluminium spoon.
Thus, 
To calculate the amount of heat released or absorbed, we use the equation:

Also,
..........(1)
where,
q = heat absorbed or released
= mass of aluminium = 39 g
= mass of coffee = 166 g
= final temperature = ?
= temperature of aluminium = 
= temperature of coffee = 
= specific heat of aluminium = 
= specific heat of coffee= 
Putting all the values in equation 1, we get:
![39\times 0.904\times (T_{final}-24)=-[166\times 4.1801\times (T_{final}-83)]](https://tex.z-dn.net/?f=39%5Ctimes%200.904%5Ctimes%20%28T_%7Bfinal%7D-24%29%3D-%5B166%5Ctimes%204.1801%5Ctimes%20%28T_%7Bfinal%7D-83%29%5D)

Hence, the final temperature of the solution is 