Angle on ramp with cart and weights on rope at end

In summary, the conversation discusses the variables nx, Ty, and (fs)y being 0, and the possibility of solving for theta if (fs)x or ny can be determined. The track is mentioned to be frictionless and the (fs) forces are to be deleted. The trigonometric functions for (F_G)_x and (F_G)_y are also brought up and the issue of them being negative is discussed. The class had clarified that g is just a scalar of 9.8 m/s^2 and the placement of negatives is uncertain. It is suggested to define the direction of positive for each variable, as long as it is consistent.
  • #1
jskrzypi
5
2
Homework Statement
A 250g cart with 250g of weight is on a ramp. Rope attached to right side going over pulley with a 50g weight on end. Calculate angle ramp needs to be at to maintain cart stationary

edit: track is frictionless
Relevant Equations
Fnetx=nx+Tx+(FG)x=0
Fnety=ny+Ty+(FG)y=0
I believe the nx, Ty, and (fs)y are all 0. I could solve for theta if I could figure out (fs)x or ny.

edit: Track is frictionless, so delete (fs) forces.

IMG_20210329_210038.jpg
 
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  • #2
You wrote ##(F_G)_x## as ##Mg\cos\theta## and ##(F_G)_y## as ##Mg\sin\theta##. Check your trig functions here. Also, shouldn't ##(F_G)_x## and ##(F_G)_y## both be negative?
 
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  • #3
I just caught the cos/sin issue. And I wasn't sure about them being negative. Obviously they are, but I may be getting it confused. Class said g is just a scalar of 9.8 m/s^2, and we need to add in the signs so it would be +(-g). I just don't know when/where to add the negatives.
 
  • #4
jskrzypi said:
don't know when/where to add the negatives.
First, you need to define which way you are taking as positive for each variable. It doesn’t matter what you choose as long as you are consistent.
I would take positive as downslope for the cart and vertically down for the suspended mass.
 

1. What is the purpose of the cart and weights on the rope at the end of the ramp?

The cart and weights on the rope at the end of the ramp are used to demonstrate the effects of gravitational force and how it affects the motion of an object on an inclined plane.

2. How does the angle of the ramp affect the motion of the cart and weights?

The angle of the ramp determines the amount of gravitational force acting on the cart and weights. The steeper the angle, the greater the force, resulting in a faster acceleration down the ramp.

3. What factors can affect the accuracy of the results from this experiment?

Some factors that can affect the accuracy of the results include the smoothness of the ramp, the weight of the cart and weights, and any external forces such as air resistance.

4. How can this experiment be modified to investigate other concepts related to motion?

This experiment can be modified by changing the angle of the ramp, adding more weights to the cart, or using different surfaces for the ramp. These modifications can help investigate concepts such as friction, mass, and the relationship between force and acceleration.

5. What are some real-world applications of this experiment?

This experiment can help us understand the physics behind objects rolling down a hill or a ramp, which can be applied to various real-world scenarios such as designing roller coasters, understanding the motion of vehicles on inclined roads, and predicting the trajectory of objects in projectile motion.

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