If mass is added to a toy car (29.7g) and dropped down a wooden ramp would it affect its speed making it go faster? I know friction comes in to play to, so if you could give me an answer or an equation to show this that would be.
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Yes, adding mass to a toy car should at least in principle make it accelerate down a ramp faster.
The total force on the car is in the "forward" direction, with magnitude $$F=m g \sin\theta\ -\ m g C_{rr}\cos\theta\ - \tfrac12 \rho v^2 C_D A\ ,$$ where $m$ is the car's mass, $g$ is the acceleration due to gravity at Earth's surface, $\theta$ is the angle from horizontal of the ramp, $C_{rr}$ is the rolling resistance coefficient, $\rho$ is the density of air, $v$ is the speed of the car, $C_D$ is the drag coefficient of the car, and $A$ is the car's cross section area. $C_{rr}$ depends on a lot of things rather than being a constant, but what's important here is that for rigid plastic tires, $C_{rr}$ should decrease with increasing $m$. $C_D$ is independent of $m$.
The first term in the above equation is the forward component of the force purely due to gravity, the second term accounts for rolling resistance, and the third term accounts for drag.
If you equate that equation with $F=ma$ and divide both sides by $m$, you get that the car's acceleration in the forward direction is
$$a=g \sin\theta\ -\ g C_{rr}\cos\theta\ - \frac{ \rho v^2 C_D A}{2 m}\ .$$
According to that equation, if $m$ increases, so does $a$.
Red Act
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According to that equation, if m increases, a decreases. m is in the denominator, what is bigger: 1/2 or 1/1000 ? – Thorsten S. Oct 04 '14 at 22:17
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2@ThorstenS. You seem to be overlooking the minus sign in front of that term. – Red Act Oct 04 '14 at 22:21
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1I am not seeming to be overlooking, I have overlooked the minus sign... #-| – Thorsten S. Oct 04 '14 at 22:38
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The gravitational acceleration is constant for all masses – mcchucklezz Nov 14 '17 at 06:06
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1@script8man Yes, the gravitational acceleration $g$ is the same constant regardless of mass. But the forward acceleration $a$ is only independent of mass if you neglect friction. Friction is usually ignored in physics classes, because it doesn't usually affect the answer by much, but the question specifically asks about the effect of friction. – Red Act Nov 14 '17 at 13:48
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If you exclude the forces of air resistance then this becomes the classic "Which falls faster? The baseball, or the cannonball?"
In the case of the cannonball and the baseball, the cannonball will have negligibly more force applied to it, but will accelerate more slowly than the baseball. In the end, they will both hit the ground at the same time.
Big force / Big mass = -9.8m/s$^2$ while Tiny force / Tiny mass also = -9.8m/s$^2$.
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Ah, then small stone falls faster, because it has lower surface area exposed to air drag. – CoilKid Oct 05 '14 at 14:28
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2No, generally it will fall slower. It has less drag, but with a lower mass the drag causes more deceleration. If they are spheres, the drag goes up as $r^2$ (the cross sectional area) while the mass goes up as $r^3$ (the volume) – Ross Millikan Oct 05 '14 at 15:05
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Right, larger stone has more momentum. Thanks, forgot about the mass for some reason. – CoilKid Oct 05 '14 at 16:04
