What minimum speed does a 100 g puck need to make it to the top of a frictionless ramp that is 3

What minimum speed does a 100 g puck need to make it to the...

Key Concepts

Conservation of Energy

This principle states that the total energy in an isolated system remains constant over time, irrespective of the transformations that occur between kinetic and potential energy. It is a foundational concept in mechanics that allows one to determine unknown quantities by equating the energy at different points along a process, provided that there is no energy loss (such as through friction).

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. It is defined by the equation KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. In problems involving motion on a frictionless surface, the initial kinetic energy is often completely converted into potential energy as the object climbs a height.

Gravitational Potential Energy

Gravitational potential energy is the energy an object has due to its position within a gravitational field, typically measured relative to a chosen reference level. It is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height gained. This concept is key when analyzing the energy changes as an object moves vertically against gravity.

Inclined Plane Geometry

The inclined plane is a common setup in physics problems which involves resolving gravitational forces along and perpendicular to the plane. Understanding the relationship between the length of the incline, the angle, and the vertical height achieved is essential. Trigonometric functions, particularly the sine function, are used to relate the ramp's angle and length to the vertical displacement.

Transcript

0:00 Hello everyone.

00:01 In this problem, we have a 100 gram puck that we're going to shoot up a ramp offland 3 meters that is inclined at 20 degrees.

00:13 So what we have to find here is the minimum velocity that the puck needs to have in order to glide up on this frictionless surface to the top of the incline.

00:25 So the minimum velocity or speed means that we want the puck to essentially stop at the top of the hill.

00:33 So we want the final speed of the puck to be zero meters per seconds.

00:37 We don't know what the initial speed is.

00:40 That's what we have to find.

00:42 And we can set up our coordinates such that the height of the puck or the initial height of the plug is at zero meters.

00:50 And then the final height of the puck is just y -a.

00:55 So we're just going to call that yf.

00:56 We can already find out what yf is in terms of the parameters that we're given because we just have a right -handed triangle over here where we have that the sign of the angle of the incline is equal to yf divided by the length of the incline.

01:12 And so l times sine alpha, so we have yf, yf is equal to l times sine alpha, where alpha in this case is of course 20 degrees.

01:23 So that's what yf is.

01:26 And then in order to find what the minimum speed has to be, there's going to be a number of concepts that we're going to use.

01:32 First of all, the kinetic energy of an object is equal to a half times the mass of the object times the speed squared...

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