# Kinetic energy Definition and 264 Discussions

In physics, the kinetic energy of an object is the energy that it possesses due to its motion.
It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.
In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is

1
2

m

v

2

{\displaystyle {\begin{smallmatrix}{\frac {1}{2}}mv^{2}\end{smallmatrix}}}
. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light.
The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound.

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1. ### What is KE of the system using F = ma ?

Homework Statement Three particles of mass all = 3 kg are located at the vertices of an equilateral triangle and are spinning about their center of mass in an empty space. The sides are length d = 2 m which doesn't change with time. Homework Equations What is the PE of the system? What is the...
2. ### 2D Elastic collision of varying mass, velocities, and angles

Problem statement: Two pucks of radius 0.05 meters collide as shown in attached picture. The mass of puck 1 is 0.1 kg and that of puck 2 is 0.15 kg. The initial velocities are v1i = 1 m/s and v2i= 0.6 m/s. (1) Assuming no friction between the pucks, only normal forces during collision, in...
3. ### Balls elastic collision off center

Problem Statement: Moe Mentum and Ken Ettik are playing pool. Moe hits the cue ball, sending it towards the 6 ball at 2 m/s. It strikes the stationary 6 ball off-center, moving off at a 60 degree angle from the original direction after a perfectly elastic collision. Both balls have a mass of...
4. ### Relationship between force and (kinetic) energy

A car of mass 1kg rests on top of a large flat mass of 1,000,000 kg (10^6 kg). They are at rest (relative to the sun) in space. The car has a battery and an electric motor with 100% efficiency. We can assume that when a torque is applied to the wheels, they roll on the surface of the flat mass...
5. ### Lagrange mechanics: Pendulum attached to a massless support

Homework Statement A simple pendulum of length ##b## and bob with mass ##m## is attached to a massless support moving vertically upward with constant acceleration ##a##. Determine (a) the equations of motion and (b) the period for small oscillations. 2. Formulas ##U = mgh## ##T = (1/2)mv^2...
6. ### Work and Rotational Kinetic Energy (Falling Chimney)

Homework Statement A tall, cylindrical chimney falls over when its base is ruptured. Treat the chimney as a thin rod of length 49.0 m. Answer the following for the instant it makes an angle of 32.0° with the vertical as it falls. (Hint: Use energy considerations, not a torque.) (a) What is the...
7. ### Conservation of energy, potential energy function

Homework Statement The potential energy for a mss m = 1.0 kg moving in one dimension is given by U(x) = (2.5J) sin πx. The mass starts at x = 0 with an initial velocity v = 0.71m/s. (The plus sign means the motion is in the positive x-direction.) Describe the subsequent motion of the mass...
8. ### An Explosive separation of two carts already in motion

Homework Statement An assembled system consists of cart A of inertia mA, cart B of inertia mB, and a spring of negligible inertia, clamped together so that the fully compressed spring is aligned between the front end of cart B and the back end of cart A. The internal energy of the system...
9. ### Frictionless shove - kinetic energy and momentum

Homework Statement Edward and Jacob, standing face-to-face on a horizontal sheet of frictionless ice, push off each other, causing each to slide backward. Jacob is more massive than Edward. After the push, which of the two is moving faster? Homework Equations Conservation of momentum: Pi = Pf...
10. ### Kinetic and potential energy in firing a cannon

Homework Statement A 20.0 kg cannonball is fired from a cannon with a muzzle speed of 1000 m/s at an angle of 37.0° with the horizontal. A second ball is fired at an angle of 90.0°. (a) Use the isolated system model to find the maximum height reached by each ball. (b) What is the total...
11. ### Physics Work & Kinetic Energy Question

Hello, I have a question regarding one of the questions on a sample exam I have for an upcoming test tomorrow. For question 2, I attempt to use the Kinetic Work Energy theorem to solve for the Work done by friction, but I don't get a correct answer. As you can see, I attempted certain things...
12. ### Block Sliding Down a Ramp that is Free to Slide

Homework Statement A block with mass m rests on a smooth, frictionless ramp with mass M and height h. The ramp itself sits on a frictionless horizontal surface in which it is free to slide. The block slides smoothly down the ramp from rest. We want to find the speed of the block after it has...
13. ### How do you know when to set work equal to change in kinetic energy or potential energy?

I have been studying the Work and Energy chapter of physics and am currently confused on when to make work equal potential energy and when to make it equal to change in kinetic energy. Some of the problems have the work equal to change in KE and some have it equal to PE. For example, why is...
14. ### Momentum versus kinetic energy

Homework Statement A 2000kg car is moving at 50km/h. What is the force required to stop it? Homework Equations KE=1/2m(v^2) p=m*v The Attempt at a Solution 1/2(2000kg)*(50km/h)^2 = 1000kg*2500km^2/h^2 = 2,500,000 km^2/h^2 converting from hours to seconds and km to m (to get joules)...