Calculating the Minimum Force for Box to Move at Constant Velocity

In summary, the conversation discusses a problem involving a force being applied to a box at an angle below the horizontal. The minimum value of the force needed to start the box's motion from rest is calculated using the formula μs*mg/cosθ-μssinθ. To maintain constant velocity, the same formula is used with μk instead of μs. A critical angle, θcrit, is introduced where the force needed becomes impossibly large. The formula for this scenario is Newton's law, where a zero sum of forces is required for constant velocity.
  • #1
Watney
7
0

Homework Statement


A force F is applied to a box of mass M at an angle θ below the horizontal (see figure). The coefficient of static friction between the box and the floor is μs, and the coefficient of kinetic friction between the two surfaces is μk.

a) What is the minimum value of F to get the box to start moving from rest?
b) What is the minimum value of F so that the box will move with constant velocity? (Assuming it's already moving.)
c) If θ is greater than some critical angle θcrit, it is impossible to have the scenario described in part b. What is θcrit ?

Homework Equations


I figured out part a which is μs*mg/cosθ-μssinθ. Then part b which is the same equation except with μk instead of μs.

The Attempt at a Solution


Honestly, I don't even know where to start. My professor has never gone over problems with critical angles. Is there a formula I can use to solve this?
 
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  • #2
Watney said:
Honestly, I don't even know where to start
Look at your answer to part b. Part c is saying that if theta is too large then no F is large enough. At what value of theta does F get impossibly large?
 
  • #3
Hi Watney, :welcome:
You start with a drawing (probably you did that already).
The formula you are looking for is called Newton's law. Constant velocity requires a zero sum of forces.

[edit] Ha! Haru was quicker and brought you even closer to your solution. Lucky you !
 

FAQ: Calculating the Minimum Force for Box to Move at Constant Velocity

1. What is the critical angle and why is it important?

The critical angle is the angle of incidence at which light is refracted and travels along the boundary between two different materials. It is important because it determines whether the light will be refracted or reflected, which is crucial in understanding the behavior of light in different mediums.

2. How is the critical angle calculated?

The critical angle is calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials.

3. What factors affect the critical angle?

The critical angle is affected by the refractive indices of the two materials, as well as the wavelength of the light and the angle of incidence. The angle of incidence must be greater than the critical angle for total internal reflection to occur.

4. How is the critical angle used in practical applications?

The critical angle is used in a variety of practical applications, such as in fiber optics, where it allows for the transmission of light over long distances without significant loss. It is also used in the design of lenses and prisms to manipulate the direction of light.

5. What happens when the angle of incidence is less than the critical angle?

When the angle of incidence is less than the critical angle, the light will be refracted and travel through the boundary between the two materials. This is the case for most everyday situations, as the critical angle is typically only reached when light travels from a more dense medium to a less dense medium.

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