A flatbed truck is carrying a heavy crate. The coefficient of static friction between the crate and the bed of the truck is 0.47. What is the maximum rate at which the driver can slow and avoid having the crate slide against the cab of the truck?
To determine the maximum rate at which the driver can slow down without having the crate slide against the cab of the truck, we need to consider the concept of static friction.
The formula for calculating static friction is:
Fs = μs * N
Where:
- Fs is the force of static friction (in this case, the maximum force the friction can withstand before the crate starts sliding)
- μs is the coefficient of static friction (given as 0.47)
- N is the normal force (the force pressing the crate against the bed of the truck)
For a crate on a flatbed truck, the normal force is equal to the weight of the crate:
N = mg
Where:
- m is the mass of the crate
- g is the acceleration due to gravity (approximately 9.8 m/s²)
To calculate the maximum rate at which the driver can slow down, we need to determine the force of static friction.
Fs = μs * N
= μs * mg
Now let's plug in the given coefficient of static friction.
Fs = 0.47 * mg
To avoid the crate from sliding against the cab of the truck, the force of static friction must be equal to or greater than the force acting on the crate due to deceleration.
Fdeceleration = ma
Where:
- a is the deceleration rate
- m is the mass of the crate
To find the maximum rate at which the driver can slow down, we need to set the force of static friction equal to the force of deceleration:
Fs = Fdeceleration
0.47 * mg = ma
Now we can solve for the deceleration rate, a:
0.47g = a
Therefore, the maximum rate at which the driver can slow down without having the crate slide against the cab of the truck is 0.47 times the acceleration due to gravity (approximately 4.616 m/s²).
To determine the maximum rate at which the driver can slow down without the crate sliding against the cab of the truck, we need to consider the maximum static friction force between the crate and the truck bed.
The maximum static friction force can be calculated using the formula:
F_max = μ_s * N
Where:
F_max is the maximum static friction force
μ_s is the coefficient of static friction
N is the normal force
In this case, since the crate is on a flatbed truck, the normal force is equal to the weight of the crate, given by:
N = m * g
Where:
m is the mass of the crate
g is the acceleration due to gravity (approximately 9.8 m/s^2)
Since the mass of the crate is not provided, we cannot directly determine the maximum rate at which the driver can slow down.