Question: What do the slope and intercept represent in a Mass vs \[1\] /acceleration?...

Question

What do the slope and intercept represent in a Mass vs $1$ /acceleration?

Answer 1

Solution

The mass of an object is inversely proportional to its acceleration, which is proportional to the net force exerted on it. The acceleration of an item grows in direct proportion to the force applied to it. As the mass of an object grows, the object's acceleration decreases.

Complete step-by-step solution:
The gradient of a graph is $\dfrac{{rise}}{{run}}$ , therefore your $y$ - axis variable is mass ( $m$ ), and your $x$ -axis variable is inverse acceleration $\left( {\dfrac{1}{a}} \right)$ , so plug them into the equation for the gradient of a straight line.
$\dfrac{m}{{\dfrac{1}{a}}}$ which is the same as $m \div \dfrac{1}{a}$
From this, we can write $m \times a$ .
Which is equal to Force ( $F = ma$ ).
As a result, the gradient represents the constant force that has been applied.
When there is an error that affects all tests, a $y$ - intercept occurs (systematic error). This is because our equation $F = ma$ has no constant at the conclusion, implying that the graph should pass through $\left( {0,0} \right)$ .
A tiny positive $y$ - intercept is seen in this situation.
This could have been due to a variety of mistakes made throughout the experiment. An extra force applied to hold the cart in place, which could be owing to the ramp being on a tiny incline, or gripping the cart with your hand are two possibilities. The scale could have been calibrated wrong, or you could have measured the mass erroneously.
The intercept could be the result of several factors. Consider something that affected all of the tests and use that as a justification.

Note: There is a continuously applied force, but more and more mass is being added. The acceleration reduces as the mass increases. This is due to Newton's second law, which states that an is inversely proportional to mass and directly proportional to force. The graph is shaped like a hyperbola. I'm not clear why the graph is a hyperbola rather than a straight line that shows a decrease as the mass grows.