![]() ![]() In this equation we easily know $m$, $g$, and $R_E$. Where $M_E$ is the mass of the earth and $R_E$ is the radius of the earth. If we equate this to Newton's universal gravitation we get We know that the weight of an object of mass $m$ on the surface of the earth is $mg$ where $g \tilde 10$ N/kg. So he could solve for it and find the mass of the Earth for the first time. Once he measured $G$ with his experiment, the only variable left in the equation was $m_1$, the mass of the earth. Because he knew how much force the Earth would exert on an apple and he knew the size of the Earth (which is $r$ in this equation - for spheres you have to measure to the center of the sphere, not the edge), Cavendish had most of the variables in the gravitational law pinned down. Why? Try setting object 1 to be Earth and object 2 to be an apple. Measuring the mass of the earthĬavendish actually thought of his experiment as a way of measuring the mass of the Earth for the first time. Newton used universal gravity to explain the orbits of planets in the solar system, and since then it has also explained things like the motion and formation of galaxies or the collapse of dust clouds into stars. It becomes important when at least one of the objects is really big, like an entire planet. In everyday life, the gravitational force between most objects is too small to notice. These vectors point opposite directions, just like Newton's third law says. Since he had measured all the masses and the distances, Cavendish was able to infer the value of $G$. Cavendish's experiment was sensitive enough that could measure the strength of the force by seeing just how much the rod and red balls twisted. The only unbalanced force on the red balls was the gravity from the big gray balls. The more force you put on those small red balls, the more the wire would twist.Ĭavendish found that the wire would twist even when he didn't put any force on it at all via pushing or pulling. The experiment was like that, but with heavy lead balls. ![]() The phone will twist right back to where it was. For example, plug your phone into its charger and hold the charging cable a foot or so above the phone, with the phone dangling underneath. Almost anything hanging from a string will behave this way. If you were to rotate the rod a bit, it would twist the wire, and the wire would exert a force to twist the balls back. The balls were balanced on a wooden rod hanging from a wire. The smaller red balls were also lead, but just 2 inches across. Lead is very dense these balls weighed 348 pounds each and were fixed in place. The two large gray balls were lead spheres about a foot in diameter. Conceptually, the experiment looked like the figure at the right. In 1797, British scientist Henry Cavendish set up a precise experiment to measure gravity. Public Domain, Link Testing universal gravitation This coefficient has no units.This vector image was created with Inkscape., For this calculation use the accepted value of the acceleration due to gravity, g = -9.81 m/sec 2. The height of the apex is recorded in your table. Use the fact that the ball was originally released from rest off of the roof which was 5.14 meters above the ground. You are to calculate the coefficient of restitution for the third ball. In our lab, it can be calculated as the ratio of |v o| for the ball rising to the apex divided by |v f | for the ball falling from its initial release off the roof. The coefficient of restitution is a measure of the speed of separation to the speed of approach in a collision. Why did the ball not bounce back up to the height from which it was originally released? How should the ball’s impact velocity when it first strikes the ground at the start of the bounce compare to its final impact velocity when it strikes the ground at the conclusion of the bounce? Support your answer. Which aspect of the data collection had the least precision: the timing or the ball's height measurement? Support your choice. Using your average experimental value for "g", calculate a percent error against the accepted value for the acceleration due to gravity at sea level, -9.81 m/sec 2. ![]() What is your group's average experimental value for "g" based on all 5 trials? ![]()
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