Question

'Suppose your hand moves upward by 0.50m while you are throwing the ball. The ball leaves your hand with an upward velocity of 20.0 m/s. Find the magnitude of the force (assumed constant) that your hand exerts on the ball. Ignore air resistance.' Now my question is not 'What is the magnitude' but rather: why did I get (roughly) the same answer using F=ma when you were supposed to use the total mechanical energy (W+K1+U1=K2+U2). So I'm more confused about how the 2 formulas are 'related', what the force actually represents in both, when to use what and if there is an actual difference.

Answer 1

The definition of acceleration  allows us to find the results for the questions about the relationship between force and energy:

• The forces is relationship to kinetic and potential energy through the work it can do.
• Energy concepts are easier to use because they are scalar.
  

Newton's second law.

Newton's second law gives a relationship between force, mass and acceleration of bodies.

             F = ma

Where F is the force, m is the mass, and a is the acceleration.

From kinematics the acceleration is defined by

           a =$\frac{dv}{dt}$  

If we use the chain rule.

          $a = \frac{dv}{dx} \frac{dx}{dt}$

         $a= v \frac{dv}{dx}$

We substitute

           F = $\frac{dv}{dx}$  

           ∫  F dx = m ∫ v dv

          ∫ F dx = ½ m v²

The term on the right is kinetic energy, therefore force and kinetic energy are related, but it is easier to use energy because it is a scalar since force is a vector quantity, it has three components.

Work is defined by the dot product of force times distance.

           W = ∫ F . d x

If we assume a system moving at constant speed, the upward force is equal to the weight of the body.

           F= W= mg

Let's substitute.

            W = m g h

The term is potential energy, therefore potential energy is equal to work and is directly related to the applied force.

In general, the concepts of energy are used when we want the result at a specific point and Newton's second law is used when we want the result at all points.

In conclusion using the definition of acceleration in kinematics we can find the results for the questions the relationship of force and energy are:

• The forces this relationship to kinetic and potential energy through the work it can do.
  

• Energy concepts are easier to use because they are scalar.

Learn more gives force and energy here: brainly.in/question/4177014