Solving Friction Problem 3: Initial Velocity of Object

[-Physician]

Homework Statement

An object takes 12.3 meters to stop because of friction. Assume no skidding. If the coefficient of static friction is 0.5, what is the initial velocity of the object?




2. The attempt at a solution
My teacher said that in this task the mass doesn't matter, so we would have
$F_{net}=ma$
$F-ug=a$
The object is on motion and we need to find v₀ so we would have
$v_0^2=v_f^2-2ax$.
Now for this we need the acceleration, so
$a=F-ug$, I have the coefficient and the gravity, but no applying force, so how can I find the acceleration, and how will I find the v₀, If I have no acceleration?

 

[genericusrnme]

Do you know about the work/energy relation?
If you do this problem becomes a lot simpler.

Regarding your attempt;
What is this F you have in your force equation
$F-ug=a$
From the conditions given I don't see what other external force is being applied other than that friction.

 

[-Physician]

Sorry for double posting I think I got it:
In this case the force of friction is the net force so (thanks to genericusrnme)
$ug=a$
$=0.5(9.81\frac{m}{s^2})=a$
$4.905\frac{m}{s^2}=a$
$v_0^2=v^2-2ax$
$v_0^2=0\frac{m^2}{s^2} - 2(4.905\frac{m}{s^2})(12.3m)$
$v_0^2=-120.663\frac{m}{s}$ (to the left)
$v_0=\sqrt{120.663}$
$v_0=10.98467113754436\frac{m}{s}$
Is that right?

 

[genericusrnme]

Yes, that is correct

 

[asteriatic]

I would first clarify the problem with my teacher to ensure that I have all the necessary information. It is important to know the specific scenario in which the object is moving and stopping due to friction, as this can affect the calculation of the initial velocity.

Assuming that the object is initially moving with a constant velocity and the only force acting on it is friction, we can use the equation $F_{net}=ma$ to determine the acceleration. The net force in this case would be the force of friction, which is equal to the coefficient of static friction multiplied by the normal force (in this case, the weight of the object). This means that the equation becomes $F_{net}=\mu_smg$, where $\mu_s$ is the coefficient of static friction and $m$ is the mass of the object.

Once we have determined the acceleration, we can use the equation $v_0^2=v_f^2-2ax$ to solve for the initial velocity. Here, $v_f$ would be zero since the object comes to a stop, and $x$ would be the distance the object travels before stopping, which is given as 12.3 meters in the problem.

It is also important to note that the assumption of no skidding may not always be accurate in real-world scenarios. If the object is not skidding, then the force of friction would be equal to the force of kinetic friction, which is typically lower than the force of static friction. This would result in a lower acceleration and a higher initial velocity for the object.

In conclusion, to solve this problem, we need to determine the net force acting on the object, use it to calculate the acceleration, and then use the acceleration in the equation for initial velocity. It is important to consider the assumptions made and clarify any uncertainties with the problem before proceeding with the solution.