A spring gun consists of a spring inside a plastic tube with spring constant, k. The spring can be compressed 20 cm from its equilibrium length. A 100 g hard plastic ball is then loaded into the tube. If the ball is shot directly up and reaches a height of 2 m above the top of the tube, what is the spring constant, k? Ignore air resistance.A) 98 N/m
B) 20 N/m
C) 12 N/m
D) 25 N/m
E) 390 N/m

Answers

Answer 1

Answer:

Answer: The spring constant is K=392.4N/m

Explanation:

According to hook's law the applied force F will be directly proportional to the extension e produced provided the spring is not distorted

The force F=ke

Where k=spring constant

e= Extention produced

h=2m

Given that

e=20cm to meter 20/100= 0.2m

m=100g to kg m=100/1000= 0.1kg

But F=mg

Ignoring air resistance

assuming g=9.81m/s²

Since the compression causes the plastic ball to poses potential energy hence energy stored in the spring

E=1/2ke²=mgh

Substituting our values to find k

First we make k subject of formula

k=2mgh/e²

k=2*0.1*9.81*2/0.1²

K=3.921/0.01

K=392.4N/m

Related Questions

Imagine that a tank is filled with water. The height of the liquid column is 7 meters and the area is 1.5square meters (m2 ). What's the force of gravity acting on the column of water? A. 73,500 N B. 102,900 N C. 68,600 N D. 110,700 N
Nuclear fusion occurs in stars. a. True b. False
When a 58g tennis ball is served, it accelerates from rest to a constant speed of 36 m/s. The impact with the racket gives the ball a constant acceleration over a distance of 35 cm. What is the magnitude of the net force acting on the ball?
A device that conveys information with analog signals and digital signals is called _____.a) an electron device b) an electrical device c) an electric device d) an electronic device
The power expended when a 10 N barbell is raised 2. 0 m in 2s is

In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga River in (Figure 1) , which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft (≈ 6.7 m) across while falling 20 ft (≈ 6.1 m).What is the minimum speed with which he’d need to run off the edge of the cliff to make it safely to the far side of the river?

Express your answer to two significant figures and include the appropriate units.

Answers

The minimum speed with which the captain Sam Brady of the US continental army had to run off the edge of the cliff to make it safely to the far side of the river is $\boxed{19.667\text{ ft/s}}$ or $\boxed{5.998\text{ m/s}}$ or $\boxed{6\text{ m/s}}$ or $\boxed{599.8\text{ cm/s}}$ .

Further explanation:

As Captain Sam Brady jumps from the cliff, he moves in two dimension under the action of gravity.

Given:

The height of free fall of the captain Brady is $20\text{ ft}$ or $6.1\text{ m}$ .

The horizontal distance moved by the captain Brady is $22\text{ ft}$ or $6.7\text{ m}$ .

Concept:

The time required to free fall of a body can be calculated by using the expression given below.

$\left( { - s}\right)=ut-(1)/(2)g{t^2}$ ……. (1)

The displacement is considered negative because the captain is moving in vertically downward direction.

Here, $s$ is the distance covered by the body in free fall, $u$ is the initial velocity of the object, $g$ is the acceleration due to gravity and $t$ is the time taken in free fall of a body.

As the Caption jumps off the cliff, he has his velocity in the horizontal direction. The velocity of the captain in vertical direction is zero.

Substitute $0$ for $u$ in the equation (1) .

$s=(1)/(2)g{t^2}$

Rearrange the above expression for $t$ .

$\boxed{t=\sqrt {\frac{{2s}}{g}}}$ …… (2)

Converting acceleration due to gravity in $\text{ft}/\text{s}^2$ .

$\begin{aligned}g&=\left( {9.81\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right)\left( {\frac{{1.0\,{\text{ft/}}{{\text{s}}^{\text{2}}}}}{{0.305\,{\text{m/}}{{\text{s}}^{\text{2}}}}}} \right) \n&=32.16\,{\text{ft/}}{{\text{s}}^{\text{2}}} \n \end{aligned}$

Substitute $20\text{ ft}$ for $s$ and $32.16\,{\text{ft/}}{{\text{s}}^{\text{2}}}$ for $g$ in equation (2) .

$\begin{aligned}t&=\sqrt {\frac{{2\left( {20\,{\text{ft}}} \right)}}{{\left( {32.16\,{\text{ft/}}{{\text{s}}^{\text{2}}}} \right)}}} \n&=1.116\,{\text{s}} \n \end{aligned}$

Therefore, the time taken by captain to free fall a height $20\text{ ft}$ is $1.116\text{ s}$ .

In the same time interval captain has to move $22\text{ ft}$ in horizontal direction. The acceleration is zero in horizontal direction. So, the velocity will be constant throughout the motion in the horizontal direction.

The distance travelled by captain in the horizontal direction is given by,

$x=v\cdot t$

Rearrange the above expression for $v$ .

$\boxed{v=(x)/(t)}$ …… (3)

Here, $x$ is the distance travelled in horizontal direction, $v$ is the velocity of the captain and $t$ is the time.

Substitute $22\text{ ft}$ for $x$ and $1.116\text{ s}$ for $t$ in equation (3) .

$\begin{aligned}v&=\frac{{22\,{\text{ft}}}}{{1.116\,{\text{s}}}} \n&=19.71\,{\text{ft/s}} \n \end{aligned}$

Thus, the minimum speed with which the captain Sam Brady of the US continental army had to run off the edge of the cliff to make it safely to the far side of the river is $\boxed{19.667\text{ ft/s}}$ or $\boxed{5.998\text{ m/s}}$ or $\boxed{6\text{ m/s}}$ or $\boxed{599.8\text{ cm/s}}$ .

Learn more:

1. Energy density stored in capacitor brainly.com/question/9617400

2. Kinetic energy of the electrons brainly.com/question/9059731

3. Force applied by the car on truck brainly.com/question/2235246

Keywords:

Free fall, projectile, gravity, 1780, Brady’s, leap, Captain, Sam Brady, US, continental army, enemies, Ohio’s, Cuyahoga river, 22 ft, 6.7 m, 20 ft, 6.1 m, minimum speed, run off, edge, cliff, safely, far side, river, 19.71 ft/s, 6 m/s, 6 meter/s, 5.99 m/s, 599.8 cm/s.

Final answer:

Using the principles of projectile motion from Physics, Captain Sam Brady would need to run with an initial horizontal speed of approximately 19.64 ft/s to reach the far side of the river.

Explanation:

This problem can be solved using basic Physics, specifically projectile motion. Here, Captain Sam Brady had to run off the edge of the cliff to make it safely to the far side of the river which is 22 ft away while falling 20 ft down. We assume that he jumps horizontally (i.e., his initial vertical velocity is 0).

Firstly, we calculate the time for the vertical fall. Using the equation t = sqrt (2h/g) where h is height and g is the acceleration due to gravity (32.2 ft/s²), we get time t ≈ 1.12s (rounded to two significant figures).

Next, we can use this time to figure out his initial horizontal velocity needed. The equation v = d/t where v is velocity, d is distance, and t is time gives us v ≈ 19.64 ft/s (rounded to two significant figures).

So, Captain Sam Brady would need to run with an initial horizontal speed of approximately 19.64 ft/s to make it safely across the river.

Learn more about Projectile Motion here:

brainly.com/question/20627626

#SPJ2

In a ballistic pendulum experiment, projectile 1 results in a maximum height h of the pendulum equal to 2.6 cm. A second projectile (of the same mass) causes the the pendulum to swing twice as high, h2 = 5.2 cm.The second projectile was how many times faster than the first?

Answers

Answer:

Second projectile is 1.4 times faster than first projectile.

Explanation:

By linear momentum conservation

Pi = Pf

m x U + M x 0 = (m + M) x V

$U= ((m + M)* V)/(m)$

Now Since this projectile + pendulum system rises to height 'h', So using energy conservation:

KEi + PEi = KEf + PEf

PEi = 0, at reference point

KEf = 0, Speed of system zero at height 'h'

$KEi = ((m + M)* V^2)/(2)$

PEf = (m + M) g h

So,

$((m + M)* V^2)/(2) + 0 = 0+ (m + M) g h$

$V =\sqrt {2gh}$

So from above value of V

Initial velocity of projectile =U

$U=((M+m)√(2gh))/(m)$

Now Since mass of projectile and pendulum are constant, So Initial velocity of projectile is proportional to the square root of height swung by pendulum.

Which means

$(U_2)/(U_1)=\sqrt{(h_2)/(h_1)}$

$U_2=\sqrt{(h_2)/(h_1)}* U_1$

$U_2=\sqrt{(5.2)/(2.6)}* U_1$

U₂ = 1.41 U₁

Therefore we can say that ,Second projectile is 1.4 times faster than first projectile.

Final answer:

In a ballistic pendulum experiment, if the pendulum swings twice as high with the second projectile as with the first, the speed of the second projectile must have been twice the speed of the first projectile.

Explanation:

In a ballistic pendulum experiment, the relation between speed of the particle and maximum height achieved by the pendulum relies on the law of conservation of energy. The kinetic energy of projectile (which is proportional to the square of the speed) gets converted into potential energy of the pendulum and hence the square of the speed of the particle is directly proportional to the maximum height achieved by the pendulum.

Given that the second projectile causes the pendulum to swing twice as high, the initial kinetic energy of the second projectile (and hence the square of its speed) must be four times that of the first. Thus, the speed of the second projectile must have been twice the speed of the first projectile, because the square root of 4 is 2.

Learn more about Ballistic Pendulum here:

brainly.com/question/35573030

#SPJ11

A car acclerates forward at 3.5m/s2 .if the car has a mass of 873 kg, whats the force applied to the car

Answers

Newton's second law.
F=ma=873*3.5=3055.5 N

Net force on the car = mass x acceleration = 873x3.5 = 3055.5N.

A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball.

Answers

The first drop makes the ball travel 16 m.
Then the maximum height decreases to 16 x 0.81
And the distance traveled is twice the distance traveled.
If we make a pattern, this forms a geometric progression in which the common ratio is 0.81 and the first term is 16.
The sum of this series: a / (1 - r)
= 16 ( 1 - 0.81)
= 84 feet
This is the upward height, and the ball returns every time so:
Total distance = 84 x 2
= 168 feet

Inertia is ______ to mass. directly proportional inversely proportional equal to not related to

Answers

Answer;

Directly proportional

Explanation

Inertia is directly proportional to mass of an object. Therefore, when the force of inertia increases the mass also increases, and when it decreases the mass also decreases.
According to Newton's first law of motion, also known as the law of inertia; a body remains at a state of rest or constant motion and in the same direction unless acted upon by an external force.
Mass of a body is totally dependent on inertia of an object, such that the more inertia an object or a body has, then the more mass it has. which means inertia and mass are directly proportional. Therefore, an object with high mass has an increased tendency to resist change in its state of motion.

Directly proportional. As mass increases, inertia increases and vice versa

Which of the following sources of energy is not renewable? wind energy
wave energy
solar energy

Answers

Answer:

all the options listed are renewable sources of energy

Explanation:

renewable sources of energy are energy sources that are easily replenished naturally such as solar energy, wind energy , wave energy even energy from rain. These sources are usually environmental friendly that non renewable energy sources

non renewable energy however, are sources of energy that will eventually run out. examples are coal, crude oil, natural gas, nuclear energy. these sources mostly pose a high risk to the environment when being used.

hope this is quite helpful?

wind energy i think, but im not for sure

Other Questions

At what speed do electromagnetic waves travel?

How could a lightbulb near an electromagnet, but not touching it, be lit? Is ac or dc required? Defend your answer.

Give me 1 example of complete inelastic collision

The color of a substance is a physical property. Please select the best answer from the choices provided T F