# The energy of a ball shot upwards

In summary, the conversation discusses the equation for mechanical energy (E(mech)=E(k)+E(g)) and how it can be used to find the velocity and height of a moving object. It also explores the use of kinematics in finding these values, and the assumption of constant velocity near the Earth's surface due to the force of gravity.

Homework Statement
The ball with a mass of 200g is shot up with the instantaneous velocity of 14 m/s.
a) Determine the mechanical energy at the point of release
b) Find the speed of the ball after it has travelled for 0.2s
c) What is the kinetic energy of the ball after 0.2s
d) Use the conservation of energy principle to determine the max height the ball reaches
Relevant Equations
E(gravity)=mgh
E(kinetic)=1/2mv^2
E(mech1)=E(g)+E(k)
E(mech1)=E(mech2)
a) E(mech)=E(k)+E(g)
E(mech)=1/2mv^2+(0.2)(9.8)(0)
E(mech)=19.6 J

b) E(mech1)=E(mech2)
E(k)+E(g)=E(k)+E(g)
E(g)=E(k)+E(g)
0=1/2mv^2+(mgh)
*No height is given so I can't solve using this method. It says instantaneous velocity meaning the velocity at 0.2s is different.

c) E(k)=1/2mv^2
E(k)=1/2(0.2)(i would use the velocity from q.b)^2

d) E(mech1)=E(mech2)
E(k)+E(g)=E(k)+E(g)
E(g)=E(k)
mgh=1/2mv^2
h=v^2/2g
h=(how would i calculate v?)^2/2(9.8)

So, I am stuck on how to calculate a few values. I can't use kinematics as this is the energy unit.

So, I am stuck on how to calculate a few values. I can't use kinematics as this is the energy unit.
I'm pretty sure that you are allowed to use kinematics to find the velocity a given time. Conservation of energy method does not consider time in its application, so clearly you need another method for that (hence: kinematics).

gneill said:
I'm pretty sure that you are allowed to use kinematics to find the velocity a given time. Conservation of energy method does not consider time in its application, so clearly you need another method for that (hence: kinematics).

I still wouldn't be able to calculate velocity for part b by using kinematics as I have 3 missing values (no acceleration, no final velocity, and no displacement). Would I have to assume that the velocity is constant?

I still wouldn't be able to calculate velocity for part b by using kinematics as I have 3 missing values (no acceleration, no final velocity, and no displacement). Would I have to assume that the velocity is constant?
Presumably the ball is assumed to be moving close to the Earth's surface. So what forces are acting on the ball?

gneill said:
Presumably the ball is assumed to be moving close to the Earth's surface. So what forces are acting on the ball?
gravity.

gravity.
Right. So given that, can you write an expression for the velocity vs time?

## What is the concept of "energy" in relation to a ball shot upwards?

The concept of energy refers to the ability of an object to do work or cause a change. In the context of a ball shot upwards, energy is used to describe the amount of force applied to the ball and the resulting motion of the ball as it moves upwards.

## What factors affect the energy of a ball shot upwards?

The energy of a ball shot upwards is affected by several factors, including the initial velocity of the ball, the mass of the ball, and the force applied to the ball. These factors determine the amount of kinetic energy that the ball possesses as it moves upwards.

## How does the energy of a ball shot upwards change as it moves upwards?

As the ball moves upwards, its energy changes from primarily kinetic energy (energy of motion) to potential energy (energy stored in its position). This change occurs because the ball is moving against the force of gravity, which slows it down and causes it to lose kinetic energy.

## What happens to the energy of a ball shot upwards when it reaches its maximum height?

At its maximum height, the ball has lost all of its kinetic energy and has only potential energy. This is because the ball has stopped moving and is at its highest point, where it has the most potential to do work. As the ball begins to fall, its potential energy will be converted back into kinetic energy.

## How is the energy of a ball shot upwards related to its trajectory?

The energy of a ball shot upwards determines the trajectory, or path, that the ball will take as it moves upwards and then falls back down. The initial energy of the ball, as well as the forces acting on it, will determine the shape and height of its trajectory. This is why a ball with more energy will travel higher and further than a ball with less energy.