What is the equilibrium force on a weight down a slope?

In summary: The force acting down the slope is the weight x sin(30), and the force acting perpendicular to the slope is the weight x cos(30).In summary, The systems shown in the figures are in equilibrium and if the spring scales are calibrated in Newtons, they will read the weight times the cosine of the angle of incline. The force acting down the slope is the weight times the sine of 30 degrees, and the force acting perpendicular to the slope is the weight times the cosine of 30 degrees.
  • #1
bettysuarez
7
0

Homework Statement


I have attached a picture of the problem to this thread, I am having trouble with part c. I am getting an answer which is much larger than 24.5N

The systems shown in the figures are in equilibrium. If the spring scales are
calibrated in Newtons, what do they read? (assume the incline in part (c) is frictionless.)

Homework Equations


Fw = mg

The Attempt at a Solution


I have attempted the solution and worked out the component of the weight force acting down the slope using Fw = mg / sin(30) = 49 / sin (30) = 98 N
 

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  • #2
Welcome to PF!

Hi bettysuarez! Welcome to PF! :smile:

(I can't see the picture yet, but …)
bettysuarez said:
I have attempted the solution and worked out the component of the weight force acting down the slope using Fw = mg / sin(30) = 49 / sin (30) = 98 N

You seem to finding the hypotenuse of a vector triangle :confused: …

they don't work that way! (not without a horizontal force :wink:).​

Just use the usual cosine formula for a component. :smile:
 
  • #3
Sorry, I'm still a bit confused... The 5 kg weight is on a 30˚ slope and the spring scale is on the slope as well. How am I supposed to work out a horizontal force? Is that the force that will be recorded by the spring scale?

Thank you!
 
  • #4
bettysuarez said:
Sorry, I'm still a bit confused... The 5 kg weight is on a 30˚ slope and the spring scale is on the slope as well. How am I supposed to work out a horizontal force? Is that the force that will be recorded by the spring scale?

No, I was saying that there's no horizontal force! :smile:

Just use the cosine formula. :wink:​
 
  • #5
Hint:

The horizontal weight is equal to the weight times the cosine of the angle of incline...
 
  • #6
bleedblue1234 said:
Hint:

The horizontal weight is equal to the weight times the cosine of the angle of incline...

erm :redface:

… no such thing as horizontal weight! :confused:​
 

Related to What is the equilibrium force on a weight down a slope?

1. How does the weight of an object affect its speed down a slope?

The weight of an object does not directly affect its speed down a slope. Instead, it is the force of gravity acting on the object's mass that determines its acceleration down the slope. A heavier object may experience a greater force of gravity, but it also has more mass to overcome that force, resulting in the same acceleration as a lighter object.

2. What factors affect the speed of an object down a slope?

The speed of an object down a slope is affected by several factors, including the slope angle, the object's mass, and the force of friction acting against it. The steeper the slope, the greater the acceleration due to gravity. A heavier object will also accelerate faster due to a greater force of gravity. Friction, however, acts in the opposite direction and can slow down the object's speed.

3. Can the mass of an object change its potential energy on a slope?

Yes, the mass of an object does affect its potential energy on a slope. The higher an object's mass, the greater its potential energy will be at the top of a slope. As the object moves down the slope, its potential energy is converted into kinetic energy, which determines its speed.

4. How does the length of a slope affect the speed of an object?

The length of a slope does not directly affect the speed of an object. Instead, it is the angle of the slope that determines the object's speed. A steeper slope will result in a faster speed due to a greater acceleration from gravity, while a shallower slope will result in a slower speed.

5. Is there a maximum speed an object can reach down a slope?

Yes, there is a maximum speed an object can reach down a slope due to the force of friction. As an object gains speed, the force of friction acting against it also increases, eventually balancing out the force of gravity and preventing the object from accelerating further. This maximum speed is known as the terminal velocity.

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