The answer is: " 208 g " .
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Explanation:
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The formula/ equation for density is:
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D = m / V ; That is, "mass divided by volume" ;
Density is expressed as:
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"mass per unit volume"; in which the "mass" is expressed in units of "g" ("grams") ; and the "unit volume" is expressed in units of:
"cm³ " or "mL";
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{Note the exact equivalent: 1 cm³ = 1 mL }.
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→ The formula is: " D = m / V " ;
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in which:
"D" refers to the "density" (see above), which is: "8.9 g/cm³ " (given);
"m" refers to the "mass" , in units of "g" (grams), which is unknown; and we want to find this value;
"V" refers to the "volume", in units of "cm³ " ;
which is: "23.4 cm³ " (given);
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We want to find the mass, "m" ; so we take the original equation/formula for the density:
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D = m / V ;
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And we rearrange; to isolate "m" (mass) on ONE side of the equation; and then we plug in our known/given values;
to solve for "m" (mass); in units of "g" (grams) ;
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Multiply each side of the equation by "V" ;
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V * { D = m / V } ; to get:
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V * D = m ; ↔ m = V * D ;
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Now, we plug in the given values for "V" (volume) and "D" (density) ; to solve for the mass, "m" ;
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m = V * D ;
m = (23.4 cm³) * (8.9 g / 1 cm³) = (23.4 * 8.9) g = 208.26 g ;
→ Round to "208 g" (3 significant figures);
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The answer is: " 208 g " .
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Thermal energy from the coffee is transferred to the mug.
acceleration = 7 m/s²
Explanation:
To determine the object's acceleration we use the following formula:
force (N) = mass (kg) × acceleration (m/s²)
acceleration (m/s²) = force (N) / mass (kg)
acceleration = 56 N / 8 kg
acceleration = 7 m/s²
Learn more about:
acceleration
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The hang time of the ball is 4.08 s
Explanation:
The ball is in free fall motion: this means that it is acted upon gravity only, so its acceleration is the acceleration of gravity,
downward (the negative sign refers to the downward direction).
Since this is a uniformly accelerated motion, we can solve the problem by using the following suvat equation:
where
v is the final velocity
u is the initial velocity
a is the acceleration
t is the time
First we calculate the time it takes for the ball to reach the maximum height, where the velocity is zero:
v = 0
Substituting:
u = +20 m/s
we find t
The motion of the ball is symmetrical, so the total time of flight is just twice the time needed to reach the maximum height, therefore:
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