Newton's 2nd Law: Doubling Force, Double Speed?

In summary, when the average force exerted on an arrow leaving a bow is doubled, the speed of the arrow will also double. However, in this specific scenario, the acceleration will double but the speed will not necessarily double. The final speed of the arrow can be calculated using the equation v = √(2F/m), where v is the final speed, F is the force, and m is the mass of the arrow. In this case, the final speed is 35.4 m/s.
  • #1
gxinxing
5
0

Homework Statement


An arrow, starting from rest, leaves the bow with a speed of 25 m/s. If the average force exerted on the arrow would be doubled, all else remains the same, with what speed would the arrow leave the bow?

Homework Equations


force = mass x acceleration


The Attempt at a Solution


Since the mass is constant, I assumed that there's a direct relationship between force and acceleration (in this case, speed, since I believe time is irrelevant) so a doubled force should have resulted in doubled acceleration (50 m/s/time). But the answer is 35.4. Why is that?
 
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  • #2
The acceleration is doubled, but the speed was asked.

ehild
 
  • #3
How do I figure out the speed without a given time?
 

Related to Newton's 2nd Law: Doubling Force, Double Speed?

1. How does Newton's 2nd Law relate to force and speed?

Newton's 2nd Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that when force is doubled, the acceleration (and therefore speed) of the object will also double.

2. Can you give an example of how doubling force results in doubling speed?

Yes, imagine a car with a mass of 1000 kg. If a force of 1000 N is applied to the car, it will accelerate at 1 m/s^2. However, if the force is doubled to 2000 N, the car will accelerate at 2 m/s^2, resulting in double the speed.

3. Is this law applicable to all objects, regardless of their mass?

Yes, Newton's 2nd Law applies to all objects, regardless of their mass. However, the same amount of force will have a greater effect on a lighter object compared to a heavier object, as the heavier object will have a greater inertia to overcome.

4. Does doubling speed also result in doubling force?

No, doubling force will result in doubling speed, but doubling speed will not necessarily result in doubling force. This is because force is also dependent on an object's mass, while speed is only dependent on the acceleration caused by the force.

5. Are there any real-life applications of this law?

Yes, Newton's 2nd Law has many real-life applications. For example, it is used in the design of vehicles, where engineers use it to determine the necessary force and acceleration needed for a vehicle to reach a certain speed. It is also used in sports, where athletes use this law to improve their performance by applying the right amount of force to achieve their desired speed.

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