How Is Static Friction Calculated from Deceleration Data?

[SciGuy26]

How would I find static friction given the following information:

V= 45km/hr
Time to decelerate completely from 45km/hr: 3.5s

The motion of the object given is of a moving vehicle. There is a cup on the dashboard inside the vehicle that moves only when deceleration time is less than or equal to 3.5s. From this information how could I solve for static friction between the cup and the dashboard?

I started by converting the velocity to m/s and found the acceleration to be be 3.57m/s^2 in the negative x direction. I do not know how to go from here...please help.

 

[Kurdt]

How is static friction defined. The maximum static friction force must occur when the cup is subject to the acceleration of 3.57 m/s².

 

[baba89]

To find the static friction between the cup and the dashboard, you will need to use the formula for Newton's Second Law: F=ma, where F is the force of friction, m is the mass of the cup, and a is the acceleration.

First, convert the velocity from km/hr to m/s by multiplying it by 1000/3600, which gives you a velocity of 12.5 m/s. Then, use the equation for acceleration, a=(vf-vi)/t, where vf is the final velocity (0 m/s) and vi is the initial velocity (12.5 m/s). This gives you an acceleration of -12.5/3.5 = -3.57 m/s^2.

Now, plug in the values for mass (m) and acceleration (a) into the formula F=ma. Since the cup is not moving vertically, we can assume that the force of friction (F) is equal to the force of gravity acting on the cup (mg). Therefore, the equation becomes mg=ma, where g is the acceleration due to gravity (9.8 m/s^2).

Solving for the static friction force (F), we get F=ma=(0.5 kg)(-3.57 m/s^2)=-1.79 N.

This means that the static friction between the cup and the dashboard is 1.79 N, which is the minimum force required to keep the cup from sliding on the dashboard during deceleration.