How Does a Spring Propelled Block Behave on a Rough Incline?

[physics587]

Homework Statement

A block of mass 2 kg is propelled by a spring with spring constant k=5200N/m onto a smooth (frictionless) track. The spring is initially compressed a distance of 0.13 m from its equilibrium configuration. At the end of the track there is a rough inclined plane at an angle of 22 degrees with respect to the horizontal and with a coefficient of kinetic friction 0.15

a) How far up the incline will the block slide before coming to rest?

b) solve using kinetic and potential energy

b) The coefficient of static friction is us= 0.7. Will the block remain at rest on the incline? If not, how fast will it be going when it reaches the bottom again?

Homework Equations

v2=2o2 +2ad

The Attempt at a Solution

1/2kx2=1/2mv2
1/2(5200)(0.13)2=1/2mv2
v=6.628

a = gsin22 - ukgcos22
a = 0.375g = 0.139 = 0.23g
a = 2.312

d = vo2/2a
d = 43.93/4.62

b) 1/2mv2 = mgh + ukmgcostheta * d
how do I calculate height?

 

[anathema]

Hi there! It seems like you're on the right track with your calculations so far. Here are some suggestions for how to proceed:

a) To find the distance up the incline, you can use the equations of motion to find the distance travelled by the block before it comes to rest. You have already found the initial velocity of the block, so you can use that to find the final velocity when it reaches the top of the incline. Then, use the equations of motion to find the distance travelled.

b) To solve using kinetic and potential energy, you can use the conservation of energy principle. At the beginning, the block has only potential energy stored in the compressed spring. At the end, the block has both kinetic energy and potential energy due to its position on the incline. You can equate these two energies to solve for the height.

To calculate the height, you can use the trigonometric relationships between the height, the angle of the incline, and the distance travelled. You can also use the Pythagorean theorem to find the height, since you know the distance travelled and the angle of the incline.

c) To determine if the block will remain at rest on the incline, you can use the equations of motion to find the acceleration of the block. If the acceleration is less than the maximum static friction force, then the block will remain at rest. If the acceleration is greater than the maximum static friction force, then the block will start sliding down the incline.

To find the velocity of the block when it reaches the bottom, you can use the equations of motion again, this time starting with the final velocity found in part a) and solving for the distance travelled.

Overall, it seems like you have a good understanding of the concepts involved in this problem. Keep up the good work!