Acceleration of a block on the floor

In summary, the block of mass m is initially stationary on a floor, with a force of magnitude F=0.540mg applied at an upward angle of θ = 21°. The magnitude of acceleration of the block across the floor is dependent on the values of s and k. To find the acceleration, a Free Body Diagram is drawn and the forces in the x and y direction are determined. The equations F=ma and F=s(N) are used to solve for N and compute the friction force. The block will only accelerate if the applied horizontal force is greater than the maximum static friction.
  • #1
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Homework Statement


The figure below shows an initially stationary block of mass m on a floor. A force of magnitude F=0.540mg is then applied at upward angle θ = 21°.



(a) What is the magnitude of the acceleration of the block across the floor if (a) s = 0.600 and k = 0.500?


(b) What is the magnitude of the acceleration of the block across the floor if s = 0.400 and k = 0.300?



Homework Equations


F=ma and F=s(N) or F=k(N)


The Attempt at a Solution



Well i drew a Free Body Diagram and found the forces in the x and y direction:

x: F(s)-Fcos(21)=0

y: mg-Fsin(21)-N=0

Then i solved for F(s)=Fcos(21)=0.54mg(cos(21))=4.94m

then i used F=s(N) to solve for N
N=8.233m

Then i set F=ma and F=s(N) equal and solved for a

a=8.233(.500)=4.11

I repeated the same steps for B...but the answers are not correct. Any help at all will be appreciated!
 
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  • #2
iamkristing said:
x: F(s)-Fcos(21)=0
This assumes equilibrium, that a = 0. Not good.

y: mg-Fsin(21)-N=0
Good. Use this to solve for N and thus compute the friction force.

The first thing to figure out is: Does it move? Compare the applied horizontal force with the maximum static friction.

If it accelerates, then use the kinetic friction to find the acceleration.
 
  • #3
Why have you set up the initial equation to be zero? For it to accelerate there has to be some sort of force there.
 

1. What is the equation for calculating acceleration of a block on the floor?

The equation for calculating acceleration of a block on the floor is a = F/m, where a is the acceleration, F is the net force acting on the block, and m is the mass of the block.

2. How does the surface of the floor affect the acceleration of a block?

The surface of the floor can affect the acceleration of a block by providing more or less friction. A rough surface will provide more friction, which can decrease the acceleration of the block, while a smooth surface will provide less friction, allowing the block to accelerate more easily.

3. What is the difference between static and kinetic friction in relation to acceleration of a block on the floor?

Static friction is the force that must be overcome to set an object in motion on a surface, while kinetic friction is the force that opposes the movement of an object that is already in motion. In relation to acceleration of a block on the floor, static friction will need to be overcome in order to start the block moving, while kinetic friction will affect the speed at which the block moves.

4. How does the mass of the block affect its acceleration on the floor?

The mass of the block directly affects its acceleration on the floor. The greater the mass of the block, the greater the force needed to accelerate it. This means that a heavier block will have a slower acceleration than a lighter block with the same amount of force applied to it.

5. Can the acceleration of a block on the floor be negative?

Yes, the acceleration of a block on the floor can be negative. This would occur if the net force acting on the block is in the opposite direction of its initial motion. In this case, the block would be decelerating or slowing down.

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