Newtons second law and stopping on a dime

In summary, the conversation discusses using the formula Σ F = -f = m*a to determine the net force necessary to stop a car of mass (m) traveling at a speed of (v) in a distance equal to the diameter of a dime (d). The correct formula is a = ((0)2 – (v)2) / 2( d – 0) * mass, and the final answer should be the magnitude of the force.
  • #1
ledhead86
59
0
An advertisement claims that a particular automobile can "stop on a dime." What net force would actually be necessary to stop an automobile of mass (m) traveling initially at a speed of (v) in a distance equal to the diameter of a dime, which is (d) ?
 
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  • #2
Σ F = -f = m*a

I used the formula v2 = v_02 + 2a(x-x_0) to find the acceleration

so a = (v2 – v_02) / 2(x-x_0) = ((0)2 – (v)2) / 2( d – 0)

then my final answer would be ((0)2 – (v)2) / 2( d – 0) * mass
 
  • #3
but apparently this is incorrect. What am I doing wrong?
 
  • #4
Looks OK to me. (Simplify the final expression, of course.)
 
  • #5
ledhead86 said:
but apparently this is incorrect. What am I doing wrong?
What makes you think this is incorrect? Also: Just find the magnitude of the force.
 
  • #6
nevermind, it was correct. I incorrectly typed it in the program
 

What is Newton's Second Law?

Newton's Second Law, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In simpler terms, the greater the force applied to an object, the greater its acceleration will be, and the more massive an object is, the less it will accelerate under the same force.

How does Newton's Second Law relate to stopping on a dime?

Stopping on a dime refers to the ability to stop an object in motion very quickly and with a short distance. According to Newton's Second Law, in order to stop an object, a force must be applied in the opposite direction of its motion. The greater the force applied, the faster the object will decelerate and come to a stop.

What factors affect the stopping distance of an object?

The stopping distance of an object is affected by several factors, including its initial speed, the mass of the object, and the amount of force applied to stop it. The surface on which the object is moving, such as a smooth road or a rough terrain, can also have an impact on the stopping distance.

How can Newton's Second Law be applied in everyday life?

Newton's Second Law has many real-world applications, such as in sports, driving, and engineering. For example, in sports like football and baseball, players use their understanding of Newton's Second Law to increase the force and acceleration of their movements, allowing them to throw, kick, or hit the ball with more power. In driving, understanding this law can help drivers make safe and efficient decisions, such as how much force to apply to the brakes to stop their vehicle in a timely manner.

Can Newton's Second Law be broken?

No, Newton's Second Law is a fundamental principle of physics and is not subject to exceptions or breaking. However, there may be instances where it appears to be broken, such as when an object seems to accelerate without any external force acting on it. In these cases, there may be other forces at play, such as air resistance or friction, that are not immediately apparent.

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