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KengaRu [80]
3 years ago
14

A scene in a movie has a stuntman falling through a floor onto a bed in the room below. The plan is to have the actor fall on hi

s back, but a researcher has been hired to investigate the safety of this stunt. When the researcher examines the mattress, she sees that it effectively has a spring constant of 77144 N/m for the area likely to be impacted by the stuntman, but it cannot depress more than 13.11 cm without injuring him. To approach this problem, consider a simplified version of the situation. A mass falls through a height of 4.12 m before landing on a spring of force constant 77144 N/m. Calculate the maximum mass that can fall on the mattress without exceeding the maximum compression distance.
Physics
1 answer:
Alina [70]3 years ago
4 0

Answer:

131 kg

Explanation:

Data:

Given,

spring constant, k = 65 144 N/m

Height of the fall = 3.32 m

Spring compression distance, x = 13. 55 × 10⁻²m

acceleration due to gravity, g = 9.81 ms⁻²

Now, during the fall, the gravitational potential energy is translated to the kinetic energy.

The kinetic energy is then later absorbed by the spring which absorbs it as the spring potential energy or simply (SPE).

Thus, the equation becomes:

Potential energy = Spring potential energy

mh (h + x) = \frac{1}{2} kx^{2} \\m(9.81 * (3.32 + 0.1311) = \frac{1}{2}*65 144 * (0.1311)^{2}  \\4.268 m = 559.82\\           m = 131 kg

maximum mass = 131 kg

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the mass of a brick is 4 kg, find the mass of water displaced by it when completely immersed in water.​
vova2212 [387]

Answer:

The correct answer is = 1.6

Explanation:

Density of water = 1000kg/m³ = d₁

Mass of brick = 4kg = m

Density of brick = 2.5 g/cm³ = 2.5 × 1000 =2500 kg/m³ = d₂

Volume of brick = m/d₂ = 4/2500 =16/10000 = 0.0016 L = v

Buoyant Force = v × d₁ × g          (g= acceleration due to gravity =9.8m/s²)

= 0.0016 × 1000 × 9.8 = 15.68 Newtons

By the Archimedes' Principle, the buoyant force is equal to the weight of the liquid displaced by an object.

Weight of the water displaced=Buoyant Force

=Mass of water displaced × g,

as weight = mass × acceleration due to gravity

15.68= mass of brick × 9.8

15.68/9.8 =Mass of water displaced

1.6 kg = Mass of water displaced

4 0
3 years ago
Question
finlep [7]

Answer:

one for physical is that your muscles will seize up or cramp when you try to move. one for mental is that if your always sitting down you will most likely become stressed or get depression

Explanation

the reason your muscles cramp is from lack of exercise form sitting they get used to that position and want to stay that way. then theres the deprestion ive had it it aint fun nor is stress ive had that too

5 0
2 years ago
Why does the density of a substance remain the same for different amount of the substance
tresset_1 [31]

Think of it this way: 
-- Any time you have something that means (some number) PER UNIT,
it doesn't matter how many units there are on the table or in the bucket,
because that amount doesn't change the (number) PER UNIT.

-- If oranges cost $1 PER POUND, it doesn't matter how many pounds
you buy, the whole bagful is still $1 PER POUND.

-- If a certain salad dressing has 40 calories PER Tablespoon, it doesn't
matter whether you eat a drop of it or drink the whole jar.  You still get
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-- Density means '(mass) PER unit of volume'.  Whether you have a tiny
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6 0
3 years ago
An engineer is designing a runway. She knows that a plane, starting at rest, needs to reach a speed of 180mph at take-off. If th
kvv77 [185]

Answer:

The plane would need to travel at least 8,\!580\; {\rm ft} (8.58 \times 10^{3}\; {\rm ft}.)

The 10,\!000\; {\rm ft} runway should be sufficient.

Explanation:

Convert unit of the the take-off velocity of this plane to \rm ft\cdot s^{-1}:

\begin{aligned}v &= 180\; {\rm mph} \\ &= 180\; {\rm mi \cdot hrs^{-1}} \times \frac{1\; {\rm hrs}}{3600\; {\rm s}} \times \frac{5280\; {\rm ft}}{1\; {\rm mi}} \\ &= 264\; {\rm ft \cdot s^{-1}}\end{aligned}.

Initial velocity of the plane: u = 0\; {\rm ft \cdot s^{-1}}.

Take-off velocity of the plane v =264\; {\rm ft\cdot s^{-1}}.

Let x denote the distance that the plane travelled along the runway. Since acceleration is constant but unknown, make use of the SUVAT equation x = ((u + v) / 2) \, t.

Notice that this equation does not require the value of acceleration. Rather, this equation make use of the fact that the distance travelled (under constant acceleration) is equal to duration t times average velocity (u + v) / 2.

The distance that the plane need to cover would be:

\begin{aligned}x &= \left(\frac{u + v}{2}\right)\, t \\ &= \frac{0\; {\rm ft \cdot s^{-1}} + 264\; {\rm ft \cdot s^{-1}}}{2} \times 65.0\; {\rm s} \\ &= 8.58\times 10^{3}\; {\rm ft}\end{aligned}.

4 0
3 years ago
Newton believed that time and space are absolute, while Einstein believed that the _______ is absolute.
8_murik_8 [283]
Speed of light 

According to Einstein, the speed of light is constant in all points of reference.  In addition, he pointed out the speed of light is the maximum speed known since in practice one can never catch up with the beam of light. This is explained by his theory of relativity. 
6 0
3 years ago
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