Newtons 2nd Law - Acceleration Problem

In summary, the problem is asking for the time it takes for a 50 kg cyclist and 10 kg bike to reach a speed of 4 m/s from a resting position, given a resultant force of 48 N. Using the equations F=ma and Vf=Vi+at, the attempt at a solution involves setting the net force (F) equal to the mass (m) times acceleration (a), and recognizing that the resultant force is the net force in this case.
  • #1
Speedking96
104
0

Homework Statement



Starting from a rest position, how long will it take a 50 kg cyclist riding a 10 kg bike to reach a speed of 4 m/s if the resultant force acting on the bicycle is 48 N?

Homework Equations



F=ma
Vf=Vi + at


The Attempt at a Solution



F=ma
(F-48)=(50+10)(a)

At this point I have to unknowns and one apparent equation.
 
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  • #2
Speedking96 said:
F=ma
(F-48)=(50+10)(a)

At this point I have to unknowns and one apparent equation.
You are told that the resultant force is 48 N, so why did you write "F - 48"?
 
  • #3
What is your reasoning for the left side of the equation?
 
  • #4
Speedking96 said:
1.
F=ma
(F-48)=(50+10)(a)


The resultant force means the net force.It's not the opposite force
 
  • #5


The equation you have written is correct. To solve for the unknowns, we can use the equation Vf=Vi+at and substitute in the values we know: Vi=0 m/s, Vf=4 m/s, a=(F-48)/(50+10). This will give us the time it takes for the cyclist to reach a speed of 4 m/s. We can then use this time in the equation d=Vit+1/2at^2 to find the distance traveled by the cyclist during this time. This problem demonstrates the relationship between force, mass, and acceleration described by Newton's Second Law. By manipulating the equations and using known values, we can solve for the unknowns and determine the time and distance traveled by the cyclist.
 

Related to Newtons 2nd Law - Acceleration Problem

What is Newton's 2nd Law of Motion?

Newton's 2nd Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. In simpler terms, the greater the force applied to an object, the greater its acceleration will be. Similarly, the more massive an object is, the less it will accelerate under the same force.

How do you calculate acceleration using Newton's 2nd Law?

The formula for calculating acceleration using Newton's 2nd Law is a = F/m, where a is the acceleration in meters per second squared (m/s^2), F is the net force in Newtons (N), and m is the mass of the object in kilograms (kg).

Can Newton's 2nd Law be applied to objects with varying mass?

Yes, Newton's 2nd Law can be applied to any object, regardless of its mass. However, the law states that the acceleration of an object is inversely proportional to its mass, meaning that the same amount of force will cause a larger acceleration in a less massive object compared to a more massive one.

What is the difference between mass and weight in relation to Newton's 2nd Law?

Mass and weight are often used interchangeably, but they are not the same. Mass is a measure of an object's resistance to acceleration, while weight is a measure of the force of gravity acting on an object. In Newton's 2nd Law, the mass of an object is used to calculate its acceleration, not its weight.

Can Newton's 2nd Law be applied to objects in free fall?

Yes, Newton's 2nd Law can be applied to objects in free fall. In this case, the force of gravity is the net force acting on the object, causing it to accelerate towards the ground. The acceleration due to gravity (g) is approximately 9.8 m/s^2 on Earth, and this value can be used in the formula a = F/m to calculate the acceleration of an object in free fall.

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