What magnitude of force must the worker apply?

AI Thread Summary
The discussion centers on calculating the force a factory worker must apply to push a 30.0-kg crate at constant speed on a level floor, considering a coefficient of kinetic friction of 0.25. The initial calculation for frictional force is correct at 73.5 Newtons, but the worker's force must account for the angle of application, which was not initially considered. The normal force is affected by the angle of the applied force, necessitating the use of trigonometric functions to resolve the worker's force into components. The correct magnitude of the force, as indicated in the textbook, is 99.2 Newtons, highlighting the importance of accurately accounting for all forces involved. Understanding the impact of the angle on the normal force is crucial for solving similar problems correctly.
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Homework Statement


A factory worker pushes a 30.0-kg crate a distance of 4.5. along a level floor at constant speed by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25. (a) What magnitude of force must the worker apply?


Homework Equations



summation of F x forces = 0

frictional force = coefficient of fric * normal force

The Attempt at a Solution



Hello, my solution is this

since the frictional force and the force of the worker in the x direction are equal,

fric force = 0.25 * 9.8 * 30 kg

fric force = 73.5 NEWTONS

so to find the magnitude of the force that the worker apply, we simply use trigonometric ratios.

cos (30) = 73.5 / r

r = 84.87 Newtons

my answer is 84.87, but the answer in the book is 99.2 Newtons. can you tell me where did i go wrong? tnx
 
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why cos(30) ? you never mentioned in your formulation of the problem that there are any angles other than 90 degree.
 
Hello, I am referreing to question 6.4a, (the one in black pen)

http://i55.tinypic.com/2e2md0z.jpg

tnx. I've tried my best but where did i go wrong? what's ur answer?
 
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blackandyello said:

Homework Statement


A factory worker pushes a 30.0-kg crate a distance of 4.5. along a level floor at constant speed by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25. (a) What magnitude of force must the worker apply?


Homework Equations



summation of F x forces = 0

frictional force = coefficient of fric * normal force

The Attempt at a Solution



Hello, my solution is this

since the frictional force and the force of the worker in the x direction are equal,

fric force = 0.25 * 9.8 * 30 kg

fric force = 73.5 NEWTONS

so to find the magnitude of the force that the worker apply, we simply use trigonometric ratios.

cos (30) = 73.5 / r

r = 84.87 Newtons

my answer is 84.87, but the answer in the book is 99.2 Newtons. can you tell me where did i go wrong? tnx
This is confusing because you posted Question 6.3(a), but show your work for 6.4 which is different because of the 30 degree downward angle of the worker's force.

The normal force is not simply the weight of the crate here. To work through a problem like this, you need to:

1. Draw a diagram showing all forces on the crate. Remember that the force from the worker is at an angle, not along the horizontal as it was in problem 6.3.

2. Set up two equations, using ƩFx=0 and ƩFy=0. Remember to separate the worker's force into components using sin and cos.

See if you can at least get that far, and if you're still stuck then post your work here for us to look at.
 
Indeed, when the worker is pushing downwards, he is increasing the weight of the crate and so the friction force as well.
 
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