Solving a 2m Inclined Plane Problem with Negligible Friction

In summary, the conversation discusses the calculation of the linear speed of a solid ball at the bottom of a 2 meter inclined plane, assuming negligible friction. The formula for potential energy (PE) is set equal to the sum of kinetic energy (KE) and rotational kinetic energy (RKE), and mass and radius terms are cancelled out. The resulting equation is then solved for v, resulting in a value of 5.3 m/s. The confusion over assumptions about friction is addressed and clarified.
  • #1
cortozld
11
0

Homework Statement


A solid ball is at the top of a 2 meter inclined plane. Assuming friction is negligible, what is its linear speed (m/s) as it reaches the bottom?


Homework Equations


PE=mgh
KE=.5mv^2
RKE=.5Iw^2
I of ball=.4mr^2
w=v/r

The Attempt at a Solution


Pretty much what i did was set PE=KE+RKE
which is mgh=.5mv^2+.5(.4mr^2)+w^2 masses cancel out and so does r when v/r is replaced with w

equation is now gh=.5v^2+.5(.4)v^2
if i solve for v i get: 2v^2=2gh/.4= v^2=gh/.4

thus v=sqrt(9.81*2/.4)

v=7.0 m/s

i really have no idea if I am doing this right...
 
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  • #2
In such problems, I find statements like "assume that friction is negligible" confusing.

If friction is really negligible, then the ball slides down the incline without rolling. In that case, it might as well be replaced by a sliding block and there is no ω.

If by "assume that friction is negligible" the intent is to indicate that the ball is actually rolling without slipping but frictional losses are negligible (i.e. mechanical energy is conserved), then the problem should state so more clearly.

Your method is correct if you assume that the latter interpretation applies.
 
  • #3
Yes, your second statement was correct. As for the problem not being specific it's my teacher not me so talk to him :). As for the answer apparently mine is wrong. So if you have any ideas about something I've missed I'd be glad to hear it
 
  • #4
cortozld said:
equation is now gh=.5v^2+.5(.4)v^2
if i solve for v i get: 2v^2=2gh/.4= v^2=gh/.4

The first line is correct. Can you show me how you get from the first line to v2=gh/0.4?
 
  • #5
From gh=.5v^2+.5(.4)v^2 I multiplied both sides by 2 to get rid of the .5: 2gh=v^2+.4v^2. Then I divided by .4 and added the v^2s together: 2gh/.4=2v^2. Divided both sides by 2 again to get: gh/.4=v^2.
 
  • #6
cortozld said:
From gh=.5v^2+.5(.4)v^2 I multiplied both sides by 2 to get rid of the .5: 2gh=v^2+.4v^2. Then I divided by .4 and added the v^2s together: 2gh/.4=2v^2. Divided both sides by 2 again to get: gh/.4=v^2.

Not correct. First you add the v2, then you divide by whatever multiplies the v2. In other words, you factor out the v2 term to get v2(1+0.4).
 
  • #7
So that means i have 2gh=v^2(1+.4). Then divide by (1+.4): 2gh/(1+.4)=v^2 and vinally solve for v. which is v=sqrt(2*9.81*2)/(1+.4)

so v=5.3 m/s! Thanks a lot :)
 

What is a 2m inclined plane problem with negligible friction?

A 2m inclined plane problem with negligible friction is a physics problem that involves calculating the motion of an object sliding down a 2m ramp with minimal resistance from friction.

What are the key principles involved in solving this type of problem?

The key principles involved in solving a 2m inclined plane problem with negligible friction include Newton's laws of motion, the concept of work and energy, and the use of trigonometry to calculate the angle of the ramp.

How do you set up the problem and determine the necessary variables?

To set up the problem, you will need to identify the mass of the object, the angle of the ramp, and the initial velocity of the object. These variables will be used in equations such as F=ma, W=Fd, and E=mv²/2 to determine the object's acceleration, work done, and final velocity.

What are the steps involved in solving a 2m inclined plane problem with negligible friction?

The steps involved in solving this type of problem include drawing a diagram of the situation, identifying the necessary variables, applying Newton's laws and energy principles to set up equations, solving for the unknown variables, and checking your answer for reasonableness.

What are some common mistakes to avoid when solving this type of problem?

Some common mistakes to avoid include forgetting to account for negligible friction, using incorrect values for the angle of the ramp, and not considering the direction of forces acting on the object. It is also important to double-check your calculations and units to ensure accuracy.

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