How Does Mass M Accelerate on a Frictionless Incline?

[VashtheStampede]

a mass M slides down a fricitionless 30 degree incline. its speed is 24m/s as it leaves the incline.

a. What is the acceleration?

 

[andrewchang]

theres no other information...?

 

[VashtheStampede]

nope. there is not

 

[VashtheStampede]

theres more questions though.

b. what is the length of the incline?

c. how long does it take to reach to floor?

 

[d_leet]

a mass M slides down a fricitionless 30 degree incline. its speed is 24m/s as it leaves the incline.
a. What is the acceleration?

Draw a free body diagram and apply Newton's laws of motion and equations of kinematics.

 

[Pyrrhus]

Start off by applying Newton's 2nd Law.

You'll find the acceleration to be $g \sin \theta$

 

[LeonhardEuler]

Presumably they want the acceleration while the block is still on the incline, otherwise the problem would truly be impossible. But actully, it is not so bad. Choose a coordinate system with the x-direction directed along the incline and the y direction pointing out from the incline. The block is not moving in the y-direction since it is niether jumping off the incline nor passing through it. Since the velocity in this direction is always zero, so must the acceleration and therefore the force. So you can disregard this direction and only look at acceleration in the x-direction. There is only one force acting: gravity, acting at an angle. It's just a matter of some geometry to find this angle. Once you have it you have the force and therefore the acceleration.

 

[andrewchang]

the other two parts can be found using kinematics.

 

[Mindscrape]

Then just use kinematics.

 

[Tide]

(a) There is sufficient information to solve the problem.

 

[VashtheStampede]

i have no idea what kinematics are. teacher never said that word.

 

[Cyrus]

If you are not sure of the word, you can always refer to a dictionary,

http://en.wikipedia.org/wiki/Kinematics