Pushing a mass up a slope and energy

Please note: knowledge of the SUVAT equations, friction and trigonometry is required for this thread.


Energy comes in many forms, and here we will focus on kinetic energy (KE) and potential energy (PE). Below are the equations of KE and PE.


change in KE = 0.5*m*[v1^2 - v2^2]

change in PE = m*g*[h2 - h1]

             where m = mass

             v1 = beginning velocity of mass

             v2 = final velocity of mass

             g = gravitational acceleration = 9.81 m/s^2

             h1 = beginning height of mass

             h2 = final height of mass


Here’s the scenario: a box is on a slope and is at rest (a velocity of 0 m/s). A man comes and pushes the box with constant force up the slope.


Let’s consider the energy of the box. Because the velocity of the box was originally 0 m/s and the man is now pushing it, which means it has some velocity because it is moving, the box’s KE has increased. Because the distance of the box from the ground has increased (the box is being pushed up the slope) the box’s PE has increased.


To find the change in KE, we will need to find the value of the beginning velocity, v1, and the value of the final velocity, v2, This can be done using the SUVAT equations and F=m*a, and I will be making a thread on these equations soon. In examples the mass will be constant and given, therefore we have everything we need to find the change in KE


To calculate PE we need the change in vertical distance of the box. This is complicated by the fact that the box is not moving in the vertical direction, but moving up a slope. Let us construct a right-angled triangle: one line being the ground (ground line), the line perpendicular (at 90 degrees) to the ground line being the change in vertical distance (vertical line) and the hypotenuse (longest line of the triangle) being the distance travelled by the mass (distance line). The angle between the slope and the ground will be the same angle the distance line makes with the ground line in our newly drawn triangle. We can calculate the distance travelled by the mass using the SUVAT equations, and thus find the length of the distance line. We can know complete our drawn triangle using trigonometry to find the length of the vertical line. The length of the vertical line is equal to the change in vertical height of the mass. Thus, we now have everything we need to find PE.


Some systems will ignore friction, perhaps because it is very small. Some systems will include friction because it is not small. Let’s say that friction is not a small term. We already know how to calculate the friction force from its equation: friction = coefficient of friction * reaction force. We also know that the work done (energy) of a body is: work done = force * distance. Substituting in the friction force to find the work done by the friction force we have: work done by friction force = coefficient of friction * reaction force * distance travelled. Thus we can now factor this into the system.


Remember the law of conservation of energy: energy cannot be created or destroyed, but can be transferred from one form (e.g. PE) to another (e.g. KE). Therefore, the changes in KE, PE and work done by friction must add up to be zero.

Daniel S. A Level Maths tutor, A Level Physics tutor, GCSE Maths tuto...

2 years ago

Answered by Daniel, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£24 /hr

Osian S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Hi, I'm Osian, a Master's student at the University of Warwick. I've had fun with mathematics from a young age, and I hope to be able to instill this passion for mathematics in you, through my tutorials! Throughout my time at Warwick,...”

£20 /hr

Tadas T.

Degree: MMathPhil Mathematics and Philosophy (Bachelors) - Oxford, St Anne's College University

Subjects offered: Maths, Philosophy and Ethics+ 5 more

Philosophy and Ethics
Further Mathematics
-Personal Statements-
-Oxbridge Preparation-

“Currently I am a third year Maths and Philosophy student at the University of Oxford. I have been interested in both Maths and Philosophy for quite a long time now and I hope I can pass both the interest and knowledge for the subject(...”

£22 /hr

Costas Y.

Degree: Electrical & Electronic Engineering (Doctorate) - Imperial College London University

Subjects offered: Maths, Further Mathematics + 1 more

Further Mathematics

“About Me: I am a 3rd year PhD student at Imperial College London studying in the Electrical and Electronic Engineering department. Ambitious and enthusiastic engineer and have a passion for mathematics and electronics. Aside from my...”

MyTutor guarantee

About the author

Daniel S.

Currently unavailable: for new students

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered: Maths, Physics


“Second year Aerospace Engineering student at Bristol. I love applying Maths and Physics to the real world for everyone to understand the environment we live in. ”

You may also like...

Posts by Daniel

Convection, conduction and radiation in space

Pushing a mass up a slope and energy

Other A Level Maths questions

How do I integrate ln(x)?

How does integration work?

How to solve the absolute-value inequalities?

What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss