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?
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To determine the minimum coefficient of static friction between the turtle and the truck bed surface, we can use Newton's laws of motion.
Here are the steps to solve this problem:
Step 1: Convert the speed from miles per hour to meters per second
- 1 mile is approximately 1609 meters
- 1 hour is 3600 seconds
- So, 55 mi/h is equal to (55 * 1609) / 3600 m/s
Step 2: Calculate the acceleration of the truck
- The truck is coming to a stop, so the initial velocity is the same as the final velocity, which is 0 m/s
- The time taken to stop, t = 12 s
- The acceleration, a = (change in velocity) / (time taken)
- The change in velocity is 0 - initial velocity = - (55 * 1609) / 3600 m/s
- Plug these values into the formula to calculate the truck's acceleration
Step 3: Calculate the net force on the turtle
- According to Newton's second law, F = m * a, where F is the net force, m is the mass of the object, and a is the acceleration
- The mass of the turtle, m = 12 kg
- Plug in the values to find the net force on the turtle
Step 4: Calculate the gravitational force on the turtle
- The gravitational force, F_gravity = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2)
- Plug in the values to find the gravitational force on the turtle
Step 5: Calculate the maximum frictional force needed to prevent the turtle from sliding
- The maximum frictional force, F_friction = F_gravity
- Since we want to find the minimum coefficient of static friction, we assume that the frictional force is the maximum possible value
Step 6: Calculate the coefficient of static friction
- The coefficient of static friction, μ, is given by the formula μ = F_friction / F_normal
- F_normal is the normal force acting on the turtle, which is equal to its weight, m * g
Step 7: Plug in the values and calculate the coefficient of static friction
By following these steps, you can find the minimum coefficient of static friction between the turtle and the truck bed surface that is needed to prevent the turtle from sliding.