What is the necessary force to move a crate on a rough surface?

In summary: Just make sure to always check your calculator settings before solving problems involving angles. In summary, the conversation discusses the process of finding the necessary force to start a large crate moving on a rough floor. The formula for calculating the force is mentioned, along with the importance of checking calculator settings when working with angles. The final answer of 207.47N is given, with the reminder to always double check calculator settings.
  • #1
miglo
98
0

Homework Statement


To move a large crate across a rough floor, you push on it with a force F at an angle of 21° below the horizontal, as shown in the figure. Find the force necessary to start the crate moving, given that the mass of the crate is m = 37 kg and the coefficient of static friction between the crate and the floor is 0.60.

Homework Equations


[tex]F_x=F\cos{\theta}[/tex]
[tex]F_y=F\sin{\theta}[/tex]
[tex]F=ma[/tex]
[tex]W=mg[/tex]
[tex]f_s=\mu_sN[/tex]

The Attempt at a Solution


so i know that [tex]\sum{\vec{F_x}}=F\cos{\theta}-\mu_sN=0[/tex]
and [tex]\sum{\vec{F_y}}=N-F\sin{\theta}-mg=0[/tex]
solving for [itex]N[/itex] i get [itex]N=F\sin{\theta}+mg[/itex] and plugging this in for N in the sum of the forces in the x direction i get [itex]F\cos{\theta}-\mu_s(F\sin{\theta}+mg)=0[/itex] and finally solving for [itex]F[/itex] i get [itex]F=\frac{\mu_smg}{\cos{\theta}-\mu_s\sin{\theta}}[/itex]
so i plugged in all the values given and yet i still got the wrong answer (my homework is online and i get 5 tries for each question)
my guess is that I am using the wrong angle, should it be 21? or 360-21=339?
or did i not solve for [itex]F[/itex] correctly?
 
Last edited:
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  • #2
Everything looks fine.

What is your final answer?

No reason to use the other angle as long as you realize the direction the component will be applied in (which you do.)
 
  • #3
i get 207.47N as my answer, but it says my answer differs from the correct answer by more than 10%
any help?
 
  • #4
Don't slap yourself, but








Your calculator is in radian mode.
 
  • #5
hahaha wow i forgot i had it in radians from my calculus 2 class this morning
thanks a lot 1MileCrash
 
  • #6
You're welcome, it happens to everyone. The important thing is that you do know how to work the problem.
 

1. What is static friction?

Static friction is a type of force that prevents objects from moving when they are in contact with each other. It is the force that must be overcome in order to set an object in motion.

2. How is static friction different from kinetic friction?

Static friction occurs when two objects are not in motion relative to each other, while kinetic friction occurs when two objects are in motion relative to each other. Static friction is typically greater than kinetic friction.

3. What factors affect the amount of static friction?

The amount of static friction depends on the materials of the two objects in contact, the roughness of their surfaces, and the amount of force being applied to one object to overcome the friction and set it in motion.

4. How is the force of static friction calculated?

The force of static friction can be calculated by multiplying the coefficient of static friction (a value that represents the roughness of the two surfaces) by the normal force, which is the force exerted by one object on the other in a direction perpendicular to their surfaces.

5. Can the force of static friction ever be greater than the applied force?

Yes, the force of static friction can be greater than the applied force if the applied force is not strong enough to overcome the maximum amount of static friction between the two objects. This is why it can be difficult to move heavy objects that are resting on a surface with high static friction.

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