Block ramp friction and spring

In summary, the problem involves a 5 kg block placed on a frictionless ramp with a 30 degree angle to the horizontal. It slides down the ramp and compresses a spring with a spring constant of 3000 N/m located 1.3 m away from the block. Using the equations for potential energy and the quadratic equation, the maximum compression of the spring can be solved for. However, there seems to be some confusion about the formula for potential energy and the use of the quadratic equation in solving the problem. Further clarification is needed to solve the problem accurately.
  • #1
bricker9236
10
0

Homework Statement


A 5 kg block is placed near the top of a frictionless ramp, which makes an angle of 30o degrees to the horizontal. A distance d = 1.3 m away from the block is an unstretched spring with k = 3000 N/m. The block slides down the ramp and compresses the spring. Find the magnitude of the maximum compression of the spring.



Homework Equations


quadratic equation ax+bx-c
h=d+xsintheta
PE=mgh=mg(d+x)sintheta
PE=1/2kx

mg(d+x)sintheta=1/2kx
0=1/2kx+-mg sintheta +-mgd sintheta
ax+bx-c


The Attempt at a Solution



What i did was plug in the numbers into the quadratic equation and i thought that is all that i had to do.. and the answer is still not correct. if someone could please help me out that would be appreciative =)
 
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  • #2
Your formula for PE is wrong. PE=1/2kx2.
You have to solve your quadratic equation of form ax2+bx+c=0.

ehild
 
  • #3
I just tried figuring it out once again..

a=1500
b=48.463
c= 63.002


so then i used the quad equation to solve for X


x= -b +- squareroot b2-4ac / 2a

and x comes out to either be

x= .0506461
x= -.0829547

then i put it back into the equation
PE=.5(k)(x)

and i tried both.. one i got around 3 and the other i got around 10

what else am i doing wrong that i can't figure this out?
 
  • #4
What does it mean "maximum compression of the spring"? And what is "x" for?

ehild
 

1. What is block ramp friction and spring?

Block ramp friction and spring is a physics concept that involves the interaction between a block or object on an inclined plane (ramp), friction between the object and the surface of the ramp, and the presence of a spring attached to the object.

2. How does friction affect the motion of the block on the ramp?

Friction acts as a resistive force that opposes the motion of the block on the ramp. It causes the block to slow down and eventually come to a stop, unless a force is applied to counteract it.

3. What is the role of the spring in this concept?

The spring provides a restoring force that acts on the block as it moves along the ramp. This force is proportional to the displacement of the block from its equilibrium position, and it helps to counteract the frictional force.

4. How does the angle of the ramp affect the motion of the block?

The angle of the ramp affects the gravitational force acting on the block, which in turn affects the normal force and the frictional force. This can impact the acceleration and velocity of the block as it moves along the ramp.

5. What are some real-life applications of block ramp friction and spring?

This concept is commonly seen in everyday objects such as door stops, car brakes, and playground slides. It is also used in engineering and design to create systems that utilize the forces of friction and springs, such as shock absorbers and conveyor belts.

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