1. A 12 weather rocket generates a thrust of 200 . The rocket, pointing upward, is clamped to the top of a vertical spring, 550 / . The spring is anchored to the ground. a. Initially, before the engine is ignited, the rocket sits at rest on the top of the spring. How much is the spring compressed? b. After the engine is ignited, what is the rocket’s speed when the spring has stretched 40 ?

a) 0.214 m (21.4 cm)

b) 1.8 m/s

Explanation:

a)

When the rocket sits on the spring, the weight of the rocket (acting downward) is balanced by the restoring force on the spring (upward).

So, we can write:

where:

- The term on the left is the weight of the rocket, with

m = 12 kg is its mass

is the acceleration due to gravity

- The term on the right is the restoring force, where

k = 550 N/m is the spring constant

x is the compression of the spring

And solving for x, we find:

Which corresponds to 21.4 cm.

b)

We can solve this part by using the law of conservation of energy.

At the beginning, when the engine is off, the rocket is at rest sitting on the spring; the total energy of the system therefore is the elastic potential energy stored in the spring, which is:

Then, when the engine is turned on, the rocket stars moving upward. The string will move from a position of x = -21.4 cm (compression) to a position of x = +40 cm (0.40 m, stretching), so the new elastic potential energy of the spring will be

Moreover, the work done by the thurst of the rocket, of magnitude F = 200 N upward, is equal to the magnitude of F time the displacement of the rocket, so

Also, the increase in gravitational potential energy of the rocket is

So, according to the law of conservation of energy, the final kinetic energy of the rocket will be:

The kinetic energy can be rewritten as

where m = 12 kg is the mass of the rocket; and solving for v, we find

  1.the balanced   chemical equation is as below

cu +   2 ag(no)₃ → cu(no₃)₂   +2 ag

2.the   much silver   produced   is   50.9 g

step 1: find the   moles of cu

moles =   mass÷   molar mass

  from periodic table the molar mass of cu = 63.5 g/mol

moles is therefore = 15.00 g÷ 63.5 g/mol = 0.236   moles

step 2: use the mole ratio to determine the   moles of ag

from equation above   cu: ag   is 1: 2

therefore the moles of ag   =0.236   moles   x 2/1 =0.472   moles

step 3: find the mass   of ag

mass = moles x molar mass

from periodic table   the molar mass of ag =107.87 g/mol

mass   = 0.472   moles x 107.87 g/mol = 50.9 g

3.   the   much   silver   collected worth is   1.797 oz

  convert   50.9 g   to oz

that is   1 gram = 0.0353 oz

          50.9 grams =?   oz

by cross multiplication

={(50.9 grams x 0.0353 oz) / 1   gram}   =1.797 oz

no sign of dia of fuel cell