Complete Question 
For each of the following scenarios, describe the force providing the centripetal force for the motion:
a. a car making a turn
b. a child swinging around a pole
c. a person sitting on a bench facing the center of a carousel
d. a rock swinging on a string
e. the Earth orbiting the Sun.
Answer:
Considering a 
     The force providing the centripetal force is the frictional force on the tires \
           i.e  
     where  is the coefficient of static friction
 is the coefficient of static friction 
Considering b
    The force providing the centripetal force is the force experienced by the boys  hand on the pole 
Considering c 
      The force providing the centripetal force is the normal from the bench due to the boys weight 
Considering d 
      The force providing the centripetal force is the tension on the string 
Considering e
       The force providing the centripetal force is the force of gravity between the earth and the sun 
Explanation:
 
        
             
        
        
        
First, let's calculate the total mechanical energy when the block is at rest and the spring is compressed 5 cm:

Now, let's use this total energy to calculate the velocity when the spring is compressed by 2.5 cm:

Therefore the speed is 1.026 m/s.
 
        
             
        
        
        
The formula for kinetic energy = ½m·v<span>2
1/2 * 55 kg x 5,87 m/s ^2 = 27.5 x </span>34.4569 = <span>947.56475 Joule </span>≈ 948 J
        
             
        
        
        
Answer: 1037 miles per hour
Explanation: In order to see the sun in the same position in the sky, you would have to travel against the speed of rotation of the earth, because this is what causes the sun to appear in a constantly changing position. 
Because of this, we will have to calculate the speed of rotation of the earth. To get started, we must know the circumference of the earth. Assuming the circumference formula for a sphere,

Where R is the radius of the earth, we find that the perimeter of the earth is approximately 24881 miles. The equation to calculate speed is given by

Because the earth completes one rotation in 24 hours, we have to find the speed of rotation as the perimeter of the earth divided by 24 hours.
The obtained result is 1037 miles per hour. 
You would have to travel at 1037 miles per hour in the direction opposite to the direction the rotation is ocurring in.