*I really don't know how to get started. I have done lots of the homework, but this one (and a couple of others) are really giving me PROBLEMS.*
A pickup truck is carrying a toolbox, but the rear gate of the truck is missing, so the box will slide out if it is sent moving. The coeffecients of kinetic and static friction between the box and the bed of the truck are 0.315 and 0.750, respectively.
Starting from rest, what is the shortest time this truck could acclerate uniformly to 28.0 m/s (approx 62.6 mph) without causing the box to slide?
Answer expressed in seconds.
I know you have to use Newton's second law to find the maximum acceleration that static friction can give the box, and then solve for the time required to reach 28 m/s, but I don't actually know HOW to do this.
Force friction= massbox*g*muStatic
This force must equal massbox*accelerationtruck.
set them equal, and solve for the acceleration of the truck.
Then,
velocityfinal=acceleration*time
solve for time.
To solve this problem, let's break it down step by step:
Step 1: Calculate the maximum static friction force that the box can experience. We can do this by using Newton's second law:
Force of static friction (Fs) = mass of the box (m) * acceleration due to gravity (g) * coefficient of static friction (μs)
Step 2: Determine the maximum acceleration that can be applied to the truck without causing the box to slide. Since the force of static friction is equal to the mass of the box times the acceleration of the truck, we can rearrange the equation to solve for the acceleration:
Fs = m * a
a = Fs / m
Step 3: Calculate the time required for the truck to reach a final velocity of 28.0 m/s. We can use the equation for linear motion:
Final velocity (vf) = initial velocity (vi) + acceleration (a) * time (t)
Given that the truck starts from rest (initial velocity is 0 m/s), we can rearrange the equation to solve for time:
t = (vf - vi) / a
In this case, vi = 0 m/s and vf = 28.0 m/s.
Step 4: Substitute the known values into the equations and solve for the desired variable.
Let's go ahead and substitute the known values:
μs = 0.750 (coefficient of static friction)
m = mass of the box
g = acceleration due to gravity (approximately 9.8 m/s^2)
vf = 28.0 m/s
First, calculate the maximum static friction force:
Fs = m * g * μs
Then, calculate the maximum acceleration:
a = Fs / m
Finally, calculate the time required:
t = (vf - vi) / a
By following these steps and substituting the known values, you should be able to find the shortest time required for the truck to accelerate uniformly to 28.0 m/s without causing the box to slide.