The gravitational force <em>F</em> between two masses <em>M</em> and <em>m</em> a distance <em>r</em> apart is
<em>F</em> = <em>G M m</em> / <em>r</em> ²
Decrease the distance by a factor of 7 by replacing <em>r</em> with <em>r</em> / 7, and decrease both masses by a factor of 8 by replacing <em>M</em> and <em>m</em> with <em>M</em> / 8 and <em>m</em> / 8, respectively. Then the new force <em>F*</em> is
<em>F*</em> = <em>G </em>(<em>M</em> / 8) (<em>m</em> / 8) / (<em>r</em> / 7)²
<em>F*</em> = (1/64 × <em>G M m</em>) / (1/49 × <em>r</em> ²)
<em>F*</em> = 49/64 × <em>G M m</em> / <em>r</em> ²
In other words, the new force is scaled down by a factor of 49/64 ≈ 0.7656, so the new force has magnitude approx. 76.56 N.
A complex machine is a machine made up of two or more simple machines that make your work easier to do. There are six simple machines from which all complex machines are made. They include: The lever. The inclined plane
No, a body can not have its velocity constant, while its speed varies. Rather, it can have its speed constant and its velocity varying. For example in a uniform circular motion.
Answer:
34.8 and 55.2º
Explanation:
This is a projectile launching exercise, as we are told that the range of the arrow must be equal to its range and = 31 m let's use the equation
The scope equation is
R = v₀² sin 2θ /g
sin 2 θ = R g / v₀²
sin 2 θ = 31 9.8 / 18²
2 θ = sin⁻¹ 0.93765
θ = 34.8º
At the launch of projectiles we have two complementary angles with the same range in this case 34.8 and (90-34.8) = 55.2º
