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3 years ago

A block of metal is 3 cm on each side. It has a mass of 283.5 grams. What is the density of the metal.

1 answer:

5 0

$Density = \frac{Mass}{Volume}
\\\rho=\frac{m}{V}
\\\\\rho=\frac{283.5}{3^3}
\\\\\rho=\frac{283.5}{27}
\\\\\rho = 10.5 g/cm^3
$

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A person jumps from the roof of a house 3.5-m high. When he strikes the ground below, he bends his knees so that his torso decel

Korvikt [17]

The force exerted on his torso by his legs during the deceleration is 4365 N.

Explanation:

Mass of the torso m=45kg

Height of the building s=3.5 m

Decelerating distance=0.71 m

when he jumps to the ground, the only acceleration is acceleration due to gravity g

motion1 from top to ground

initial velocity u=0

we have to calculate final velocity v using the following equation of motion.

$v^2-u^2=2gs\\v^2-0^2=2\times 9.8\times3.5=68.6\\v=\sqrt{68.6} \\=8.3$

use height of the building as the distance s as the jump from top to the ground is only described here.

Motion 2 on the ground

v=0

u=8.3(final velocity of motion 1)

The deceleration after striking the ground can be calculated from the equation of motion

$v^2-u^2=2as\\\\a=v^2-u^2/2\times 0.71\\=0^2-8.3^2/0.71=97 m/s^2$

The decelerating distance is used in the place of s since since the motion after hitting the ground is described in this case.

The equation of force is

$F=ma\\=45\times 97=4365 N$

6 0

3 years ago

Earth has a mass of 5,970,000,000,000,000,000,000,000 kg. How would

mr Goodwill [35]

Answer:

5.97×10^24 kg

Explanation:

thats how it is expressed

7 0

3 years ago

Two asteroids collide and stick together. The first asteroid has mass of 1.50 × 104 kg andis initially moving at 0.77 × 103 m/s.

KengaRu [80]

Answer:

Magnitude 900m/s, direction 12.8° respect to the velocity of the first asteroid.

Explanation:

This is a perfectly inelastic collision, because the two asteroids stick together at the end. That means that the kinetic energy doesn't conserves, but the linear momentum does. But, since the velocities of the asteroids have different directions, we have to break down them in components. For convenience, we will take the direction of the first asteroid as x-axis, and its perpendicular direction (in the plane of the two velocity vectors) as y-axis. So, we have that:

$p_{1ox}+p_{2ox}=p_{fx}\\\\p_{2oy}=p_{fy}$

And, since $p=mv$ , we get:

$m_1v_{1o}+m_2v_{2o}\cos\theta=(m_1+m_2)v_{fx}\\\\m_2v_{2o}\sin\theta=(m_1+m_2)v_{fy}$

Solving for v_fx and v_fy, and calculating their values, we get:

$v_{fx}=\frac{m_1v_{1o}+m_2v_{2o}\cos\theta}{m_1+m_2}\\\\\implies v_{fx}=\frac{(1.50*10^{4}kg)(0.77*10^{3}m/s)+(2.00*10^{4}kg)(1.02*10^{3}m/s)\cos20\°}{1.50*10^{4}kg+2.00*10^{4}kg}=878m/s\\\\\\v_{fy}=\frac{m_2v_{2o}\sin\theta}{m_1+m_2}\\\\\implies v_{fy}=\frac{(2.00*10^{4}kg)(1.02*10^{3}m/s)\sin20\°}{1.50*10^{4}kg+2.00*10^{4}kg}=199m/s$

Now, the final speed can be calculated using the Pythagorean Theorem:

$v_f=\sqrt{v_{fx}^{2}+v_{fy}^{2}} \\\\\implies v_f=\sqrt{(878m/s)^{2}+(199m/s)^{2}}=900m/s$

And the direction $\beta=\arctan \frac{v_{fy}}{v_{fx}}\\ \\\implies \beta=\arctan\frac{199m/s}{878m/s}=12.8\°$ can be obtained using trigonometry:

$\beta=\arctan \frac{v_{fy}}{v_{fx}}\\ \\\implies \beta=\arctan\frac{199m/s}{878m/s}=12.8\°$

That means that the final velocity of the two asteroids has a magnitude of 900m/s and a direction of 12.8° with respect to the velocity of the first asteroid.

7 0

3 years ago

Why must chemical rxn be balanced

Svetradugi [14.3K]

The chemical equation needs to be balanced so that it follows the law of conservation of mass. A balanced chemical equation occurs when the number of the different atoms of elements in the reactants side is equal to that of the products side. Balancing chemical equations is a process of trial and error.

5 0

3 years ago

A body of mass 2.78 kg is pushed straight upward by a 31.3 N vertical force. What is its acceleration (in m/s2)

Bingel [31]

To solve this problem we will apply the concepts related to Newton's second law for which the product of mass and acceleration is defined as the force applied to an object. Mathematically this is,

$F_{net} = ma \rightarrow a = \frac{F_{net}}{m}$