Go Back   Physics Help Forum > High School and Pre-University Physics Help > Energy and Work

Energy and Work Energy and Work Physics Help Forum

Reply
 
LinkBack Thread Tools Display Modes
Old Dec 3rd 2009, 05:42 PM   #1
Junior Member
 
Join Date: Dec 2009
Posts: 1
Find speed of block on a ramp/pulley

A 20kg block (m1) slides on a 40 degree frictionless ramp. This block is connected to a 30kg block (m2) by a string that passes over a frictionless pulley. The 30kg block is 20cm above the floor and connected to a spring of negligible mass with spring constant 250N/m. The spring is initially unstretched and connected to the floor. The 20kg block is pulled a distance of 20cm down the ramp (so that the 30kg block is 40cm above the floor) and is released from rest. Calculate the speed of each block when the 30kg block is again 20cm above the floor (spring unstretched).

My attempt:
I assumed that you had to use conservation of energy to find v:
Usi + Ugi +KEi = Usf + Ugf + KEf,
where Us is Spring potential, Ug is gravitational potential and KE is kinetic energy.

KE is initially zero so we have
0.5k(xi)^2 + mghi = 0.5k(xf)^2 + mghf + 0.5mv^2

xi is 0.2m, xf is 0.4m for block 2.
I worked everything out and got 10v^2 = -64...which I'm pretty sure is incorrect. Can anyone guide me to the right direction??

Thanks!!
tom1030 is offline   Reply With Quote
Old Dec 4th 2009, 01:18 AM   #2
Physics Team
 
Join Date: Feb 2009
Posts: 1,425
Let us first look at the problem in the absence of the spring.

Let a be the accln of the system and T be the tension in the string


We have for the 20 kg block

T - 20 g sin 40 = 20 a and

30 g - T = 30 a for the 30 kg block.

Eliminating T we find that the accln a = 3.36 m/sec.

Without the spring, the motion of the 30 kg block would be identical to that on a planet where g = 3.36 m/s if it were falling freely.

Let the potential be zero at 20 cm above the floor.

When the block is pulled up by 20 cm its effective increase in grav P.E. on that planet will be 30 x 3.36 x 0.02.

But in fact it is connected to a spring, and the extension results in an additional P.E. of 0.5 x 250 x (0.02)^2.

Thus the total P.E. is

30 x 3.36 x 0.02 + 0.5 x 250 x (0.02)^2 = 2.066.

from conservation of energy, this must be equal to the K.E. when it reaches back to 20 cm above the floor. Hence

0.5 x 30 x v^2 = 2.066 giving v = 0.371 m/s or 37.1 cm/sec.

Is the answer OK ?
physicsquest is offline   Reply With Quote
Reply

  Physics Help Forum > High School and Pre-University Physics Help > Energy and Work

Tags
block, find, ramp or pulley, speed



Thread Tools
Display Modes


Similar Physics Forum Discussions
Thread Thread Starter Forum Replies Last Post
experiment to find the acceleration of an object down a ramp njuice8 Kinematics and Dynamics 3 Jun 14th 2013 01:10 PM
Acceleration of a block on a pulley with mass alongtheway Periodic and Circular Motion 2 Apr 1st 2013 08:01 PM
A 15 kg block with a pulley attached slides along a frictionless surface. rodjav305 Kinematics and Dynamics 8 Nov 30th 2010 05:48 PM
Block hanging from a pulley deeds025 Kinematics and Dynamics 1 Oct 7th 2009 12:20 AM
Block Slides Down Ramp and Off Table strgrl Kinematics and Dynamics 6 Apr 18th 2009 03:08 AM


Facebook Twitter Google+ RSS Feed