How Do You Calculate Final Velocity and Time for an Object on a Sloped Surface?

[murphy1935]

Homework Statement

A 20kg object is on a 10 m long, 15 degree slope , that has a coefficient of friction that is 0.2 Calculate the time to slide down the final velocity at the bottom

2. Homework Equations [/b

Fg=mag
Fn=Fgcos(theta)
Fp=Fgsin(theta)
mu=Ff/Fn
Fr=MAr

The Attempt at a Solution

I have gotten to the Fr=MAr stage, but after that where you substitute for Vf, Vi, S, Ar, and T; I have gotten stuck.

Any hints or tips would be greatly appreciated, thanks for your time

 

[rock.freak667]

Find the resultant acceleration.
Find the final velocity with conservation of energy.
Use v=u+at and find t.

 

[nlightner]

.

As a scientist, it is important to approach problems like this systematically and logically. In this case, we are dealing with an object on a slope, so we can use the equations for Newton's second law and the equations for motion along an inclined plane to solve for the final velocity and time.

First, we need to draw a free body diagram of the object on the slope. We can see that there are three forces acting on the object: the gravitational force (Fg), the normal force (Fn), and the force of friction (Ff). The gravitational force can be calculated using Fg = mg, where m is the mass of the object and g is the acceleration due to gravity.

Next, we need to break down the gravitational force into its components along and perpendicular to the slope. We can use trigonometry to find that Fgx = Fgcos(theta) and Fgy = Fgsin(theta). The normal force is equal and opposite to the perpendicular component of the gravitational force, so Fn = Fgy.

Using the given coefficient of friction (mu = Ff/Fn), we can calculate the force of friction as Ff = muFn. Finally, we can use the equation for Newton's second law (Fnet = ma) to set up an equation for the acceleration of the object along the slope: Fnet = Fgx - Ff = ma.

Now, we can use the equations for motion along an inclined plane to solve for the final velocity and time. We know that the acceleration of the object is equal to the component of gravity along the slope (a = gsin(theta)). We also know that the displacement of the object along the slope is 10 m. Using the equation vf^2 = vi^2 + 2as, we can solve for the final velocity at the bottom of the slope (vf). Then, using the equation d = vit + 1/2at^2, we can solve for the time it takes for the object to slide down the slope (t).

In summary, as a scientist, it is important to break down a problem into smaller steps and use the appropriate equations and principles to solve for the desired quantities. In this case, we used Newton's second law and the equations for motion along an inclined plane to solve for the final velocity and time of an object sliding down a slope with friction.