A 12-kg turtle rests on the bed of a zookeeper’s truck, which is traveling down a country road at 55 mi/h. The zookeeper spots a deer in the road, and slows to a stop in 12 s. Assuming constant acceleration, what is the minimum coefficient of static friction between the turtle and the truck bed surface that is needed to prevent the turtle from sliding?
F=ma
mu(mg)=ma
for a, change 55mi/hr to m/s
a=changevelocity/timeinseconds
solve for mu.
so i change 55m/hr to 11m/720s. to solve for mu i times that by 12? then i get 11m/60s??
Good lord.
Put this int he google search window:
55miles/hr in m/s
Then use that (about 24m/s)
mu*g=(24-0)/12
mu= 2/9.8 about .2
To find the minimum coefficient of static friction needed to prevent the turtle from sliding, we can use Newton's second law of motion and apply it to the turtle.
1. First, let's calculate the acceleration of the truck. We know that the truck starts from a speed of 55 mi/h and comes to a stop in 12 seconds.
To convert the speed from mi/h to m/s:
55 mi/h * (1609.34 m/1 mi) * (1 h/3600 s) = 24.587 m/s
To calculate the acceleration of the truck:
acceleration = (change in velocity) / (time) = (0 - 24.587 m/s) / (12 s) = -2.048 m/s^2 (negative sign because the truck is slowing down)
2. Now, let's consider the turtle's motion. The force acting on the turtle is the force of friction. According to Newton's second law, the net force on an object is equal to its mass multiplied by its acceleration. Since the turtle is at rest, the net force must be zero.
The force of friction can be calculated using the equation: force of friction = coefficient of static friction * normal force
Since the vertical forces are balanced, the normal force on the turtle is equal to its weight. The weight of the turtle can be calculated using the equation: weight = mass * g, where g is the acceleration due to gravity (~9.8 m/s^2).
normal force = weight = 12 kg * 9.8 m/s^2 = 117.6 N
3. We can now use Newton's second law to find the force of friction acting on the turtle.
force of friction = mass * acceleration = 12 kg * -2.048 m/s^2 = -24.576 N
4. Finally, we can determine the coefficient of static friction by dividing the force of friction by the normal force.
coefficient of static friction = force of friction / normal force = -24.576 N / 117.6 N ≈ -0.209
Since the coefficient of friction cannot be negative, we take the positive value:
coefficient of static friction ≈ 0.209
Therefore, the minimum coefficient of static friction between the turtle and the truck bed surface that is needed to prevent the turtle from sliding is approximately 0.209.