What is the Acceleration of a Pushed Crate with Friction?

In summary, a 200kg crate is pushed horizontally with a force of 700 N, and has a coefficient of friction of 0.20. After calculating the magnitude of the friction force and the net force, the acceleration of the crate is found to be 5.462 m/s^2 due to an error in using the minus sign for the acceleration due to gravity. The correct solution is 3.3 m/s^2, as friction reduces the effect of the applied force.
  • #1
A 200kg crate us pushed horizontally with a force of 700 N. If the coefficient of friction is 0.20, calculate the acceleratio of the crate.

I tried doing this but I don't seem to be getting the right answer.

m = 200 kg
f(app)= 700 N
U = 0.20
Ff = (0.20)(200)(-9.81)
=-392.4 N
Fnet = 700-(-392.4)
= 1092.4 N
Fnet = mass x acceleration
1092.4 = 200 (a)
5.462 m/s^2 = a

The answer booklet says that I should be getting 3.3m/s^2 as my answer.
 
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  • #2
drinkingstraw said:
m = 200 kg
f(app)= 700 N
U = 0.20
Ff = (0.20)(200)(-9.81)
=-392.4 N
Your error is giving g a minus sign. g is just the magnitude of the acceleration due to gravity.

So friction = μN = μmg. That's just the magnitude of the friction force. It's up to you to assign it the proper direction and sign; since it opposes the motion it will be negative (assuming the crate moves in the positive direction).

Set ΣF = ma and solve for a.

(In a nutshell: The friction reduces the effect of the applied force.)
 

1. What is friction?

Friction is a force that opposes the motion between two surfaces in contact. It is caused by the interactions between the microscopic bumps and ridges on the two surfaces.

2. How does friction affect acceleration?

Friction acts in the direction opposite to the motion, so it can decrease the acceleration of an object. The amount of friction depends on the surface materials and the force pushing the objects together.

3. What factors affect the amount of friction between two surfaces?

The amount of friction between two surfaces depends on the nature of the surfaces, the force pressing them together, and the roughness of the surfaces.

4. How can friction be reduced?

Friction can be reduced by using lubricants, such as oil or grease, between the surfaces. It can also be reduced by making the surfaces smoother or by using materials that have lower coefficients of friction.

5. Can friction ever be beneficial?

Yes, friction can be beneficial in many cases. It helps us to walk, drive, and grip objects. Without friction, it would be difficult to perform everyday tasks. Friction also plays a crucial role in stopping moving objects, such as cars or bicycles, by converting their kinetic energy into heat.

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