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nordsb [41]
3 years ago
14

Old naval ships fired 14 kg cannon balls from a 250 kg cannon. It was very important to stop the recoil of the cannon, since oth

erwise the heavy cannon would go careening across the deck of the ship. In one design, a large spring with spring constant 2.0×10^4 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to the ship's frame.
What was the speed (in m/s) of the cannon ball if the spring compressed 56 cm when the cannon was fired?
Physics
1 answer:
Talja [164]3 years ago
8 0

Answer:

Speed of canon ball = V = 89.443 m/s

Explanation:

the spring potential energy will be converted into kinectic energy

M= mass of cannon

m= mass of cannon balls

k= 2.0*10^4 N/m

compression x= 0.56 m

0.5kx^2 = 0.5Mv^2

2 x 10^4 x 0.56^2 = 250 x v^2

Speed of canon = v = 5.008 m/s

Now,

we have, by momentum consevation

m x 0 + M x 0 = mV - Mv

0 = 14 x V - 250 x 5.008

Speed of canon ball = V = 89.443 m/s

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reviews the approach taken in problems such as this one. A bird watcher meanders through the woods, walking 0.916 km due east, 0
Verizon [17]

Answer:

Displacement: 2.230 km    Average velocity: 1.274\frac{km}{h}

Explanation:

Let's represent displacement by the letter S and the displacement in direction 49.7° as A. Displaement is a vector, so we need to decompose all the bird's displacement into their X-Y compoments. Let's go one by one:

  • 0.916 km due east is an horizontal direction and cane be seen as  direction towards the negative side of X-axis.
  • 0.928 km due south is a vertical direction and can be seen as a direction towards the negative side of Y-axis.
  • 3.52 km in a direction of 49.7° has components on X and Y  axes. It is necessary to break it down using trigonometry,

First of all. We need to sum all the X components and all the Y componets.

∑Sx = Ax -0.916 ⇒  ∑Sx = [tex]3.52cos(49.7) - 0.916

∑Sx = 1.361 km

∑Sy = Ay - 0.918 ⇒ ∑Sy = 3.52sin(49.7) - 0.918

∑Sy = 1.767

The total displacement is calculated using Pythagoeran therorem:

S_{total} =\sqrt{Sx^{2}+ Sy^{2} } ⇒

S_{total} = 2.230 km

With displacement calculated, we can find the average speed as follows:

V = S/t  ⇒  V = \frac{2.230}{1.750}

V = 1.274\frac{km}{h}

7 0
3 years ago
If a town was 90 miles away and you travel at 45 mph how long would it take to get there
notka56 [123]

Answer:

t = 2 hours

Explanation:

Given that,

Distance of the town, d = 90 miles

Speed, v = 45 mph

We need to find the time to get there. The speed of an object is given by :

v=\dfrac{d}{t}

Where

t is time

t=\dfrac{d}{v}\\\\t=\dfrac{90}{45}\\\\t=2\ h

So, the required time is 2 hours.

5 0
3 years ago
A gas sample is confined within a chamber that has a movable piston. A small load is placed on the piston; and the system is all
timurjin [86]

Explanation:

It is given that,

Total weight of the piston, W = F = 70 N

Area of the piston, a=5\times 10^{-4}\ m^2

Let P is the pressure exerted on the piston by the gas. The force per unit area is called the pressure exerted pressure of the gas. Mathematically, it is given by :

P=\dfrac{F}{A}

P=\dfrac{70\ N}{5\times 10^{-4}\ m^2}

P=1.4\times 10^5\ Pa

We know that the atmospheric pressure is given by :

P_o=1.013\times 10^5\ Pa

So, the pressure is given by :

p=P+P_o

p=1.4\times 10^5+1.013\times 10^5

p=2.41\times 10^5\ Pa

Hence, this is the required solution.

7 0
3 years ago
Use V=Voe^-t/RC and T=RC to derive T1/2=Tln2
Ksju [112]
Enclosed is some guidance algebra.I find this q a little confusing. It quotes "RC" which usually makes me think of electrical circuits and time constants based on converting calculating RC value and equating that to t for one time constant then 2RC for two time constants etc. The theory being that after 5 time constants - 5RC - a circuit is stable. BUT, this q then goes on to mention HALF LIFE. The curves for both half life and time constant are both exponential, as in the number e to the power of something, but the algebra is slightly different. I hope my algebra is ok.

3 0
3 years ago
An 80-kg hiker climbs to the top of a tall hill and builds up 470,000 J of gravitational potential energy. How high did the hike
nekit [7.7K]

Answer:

599 meters is the answer rounded to the nearest whole number and 599.489795918 meters is the complete answer

Explanation:

to find gravitational potential energy you multiply mass x acceleration due to gravity (always 9.8 on earth) x hight

since we know the gravitational potential energy and want to find out the hight, we take the gravitational potential energy (470,000) and divide it by the product of acceleration due to gravity x mass (9.8 x 80)

so how high the hiker climbed is equal to 470,000 divided by (9.8 x 80)

hight = 470,000 / (9.8 x 80)

hight = 470,000 / 784

hight = 599.489795918 meters

as for rounding, if the decimal is less than 5 you round "down" and keep the current whole number, if the decimal is 5 or greater you round "up" and add 1 to get your new number

5 0
3 years ago
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