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1 year ago

Given two objects of the same mass but of different sizes, which object has a greater density?

1 answer:

4 0

Given two objects of the same mass but of different sizes, the one that has a greater density is: a. the smaller object

Due to the density of an object is the relation that exist between the mass and the space that the object occupies, if we have two objects with the same mass the one that is going to have a greater density is the smaller object because it occupies less space with more mass.

We can prove it using the density formula to solve the following exercise:

Two objects have a mass of 100 g, and their volume are 20 cm³ and 10 cm³ respectively, what is the density of each one?

The general formula of the density is:

d = m/v

Where:

d= density
m= mass
v= volume

Information about the problem:

m = 100 g
v1= 20 cm³
v2=10 cm³
d1=?
d2?

Applying the density formula we get:

d = m/v

d1 = 100g/20 cm³

d1 = 5g/cm³

d2 = 100g/10 cm³

d2 = 10g/cm³

With the results we can confirm that the object that has the greater density is the smaller, because it has less volume.

<h3>What is density?</h3>

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

Learn more about density in: brainly.com/question/1354972

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A 5.00 kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force F(t) is applied to the en

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The velocity of the crate vs time is given by the derivative of the position, so it is:

$v(t)=y'(t)=\frac{d}{dt}(2.80t+0.61t^3)=2.80+1.83t^2$

Similarly, the acceleration of the crate vs time is given by the derivative of the velocity, so it is:

$a(t)=v'(t)=\frac{d}{dt}(2.80+1.83t^2)=3.66t$ [m/s^2]

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3 years ago

Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed v

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$p=mv$

where

m is the mass of the object

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$p_1 = m_1 v_1 = (2m)(v)=2mv$

Object 2 has a mass of $m_2 = m$ and a speed of $v_2 = \sqrt{2} v$ , so its momentum is

$p_2 = m_2 v_2 = (m)(\sqrt{2} v)=\sqrt{2}mv$

So we see that $p_1 > p_2$ , so object 1 has the greater momentum.

2) The objects have the same kinetic energy.

The kinetic energy of an object is given by

$K=\frac{1}{2}mv^2$

where

m is the mass of the object

v is its speed

Object 1 has a mass of $m_1 = 2m$ and a speed of $v_1 = v$ , so its kinetic energy is

$K_1 = \frac{1}{2}m_1 v_1^2 = \frac{1}{2}(2m)(v)^2=mv^2$

Object 2 has a mass of $m_2 = m$ and a speed of $v_2 = \sqrt{2} v$ , so its kinetic energy is

$K_2 = \frac{1}{2}m_2 v_2^2 = \frac{1}{2}(m)(\sqrt{2} v)^2=mv^2$

So we see that $K_1 =K_2$ , so the objects have same kinetic energy

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