Newton's Laws Question: Skateboard Speeds After Release | F=ma Explained

In summary, Jack and Jill are on skateboards. Jack weighs 3 times heavier than Jill, and is pushing Jill(a horizontal force on Jill's back). Immediately after Jack let's go, they're moving away from each other at different speeds. Assuming no friction, Jack's speed is 3 times greater than Jill's at the start, but at t=0, their speeds are equal.
  • #1
beancurd
3
0
Jack and Jill are on skateboards. Jack weighs 3 times heavier than Jill, and is pushing Jill(a horizontal force on Jill's back). Immediately after Jack let's go, what are the speeds they're moving at? (No need to take friction into consideration)

F=ma
Okay, I do understand that they will be moving away from each other, and that Jill's acceleration will be 3 times faster than Jack. But that does not mean that Jill's speed is three times faster than Jack IMMEDIATELY after he let's go, right?I think they will have equal speed... but I'm not sure. Can someone answer this question?
 
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  • #2
Welcome to PF!

What principle do you think apply here? Can you write up an equation modelling that principle for Jack and Jills speed and mass?
 
  • #3
Newton's third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear

F= ma for Jill and
F = 3ma for Jack

Since force is the same, I know that the magnitude of acceleration of Jill will be three times greater than Jack's. Generally at any given time then, Jill's speed will be three times greater than Jack's. But at t=0, the initial speed? That, I'm not too sure. My guess is that the initial speed of both Jack and Jill should be the same...

Yeah.. that's all I know.
 
  • #4
You are correct about the accelerations of Jack and Jill, and I agree that it makes most sense to assume their relative speed is zero to start with.

I assumed before that you had heard of momentum and the principles associated with it, but if not, you can assume that F is constant over a small time interval t and use that to prove that their speeds also are opposite and a factor three different in magnitude (assuming you know how to find the speed increase from an object under constant acceleration as a function of time).
 
  • #5
Ah, I see. Thank you for your help.
 

1. What are Newton's Laws of Motion?

Newton's Laws of Motion are a set of three physical laws that describe the behavior of objects in motion. They were published by Sir Isaac Newton in 1687 and are a fundamental concept in the field of physics.

2. What is the First Law of Motion?

The First Law of Motion, also known as the Law of Inertia, states that an object at rest will remain at rest and an object in motion will continue to move in a straight line at a constant velocity, unless acted upon by an external force.

3. What is the Second Law of Motion?

The Second Law of Motion 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 the greater the force applied to an object, the greater its acceleration will be.

4. What is the Third Law of Motion?

The Third Law of Motion, also known as the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal but opposite force back on the first object.

5. How are Newton's Laws used in everyday life?

Newton's Laws of Motion have numerous applications in everyday life. For example, the First Law explains why objects on a flat surface will stay at rest or continue moving in a straight line unless acted upon by a force. The Second Law is used to calculate the force needed to move an object, such as when pushing a shopping cart. The Third Law is seen in actions such as walking, where the ground exerts an equal and opposite force back on our feet, allowing us to move forward.

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