Block, Ramp, Friction, and Spring work done

In summary: The man pulls a block of mass 20 kg up an incline at a slow constant velocity for a distance of 3.5 m. The incline makes an angle 33° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is 0.2.a) What is the work Wm done by the man?The work done by the man is 823.919 J.b) What is the speed v of the block when it first reaches the horizontal surface?The speed of the block when it first reaches the horizontal surface is 9.81 m/s.c) What is the spring constant k of the spring?The spring constant
  • #1
Awwnutz
43
0
http://img412.imageshack.us/img412/7050/blockspringrampfrictionfy0.gif

A man pulls a block of mass m = 20 kg up an incline at a slow constant velocity for a distance of d = 3.5 m. The incline makes an angle q = 33° with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is µk = 0.2.

a) What is the work Wm done by the man?

b) What is the speed v of the block when it first reaches the horizontal surface?

c) What is the spring constant k of the spring?

d) How far up the incline d1 does the block rebound?


Relevant equations:
Wtotal = Change in Kinetic energy
Ffriction = Coefficient of friction(Fnormal)
Fspring = kx
(1/2)mv^2

I know there are the force of friction, the man, and gravity on the box. I started by saying:
Wman - Wgrav - Wfriction = Change in KE
Wgrav = m*g(in x-direction)*(Change in height) -->(20kg)(9.81m/s^2*sin33)(3.5sin33m)
Wfriction = (coefficient of friction)*m*g*distance -->(.2)(20kg)(9.81m/s^2)(3.5m)
Change in KE = 0
Wman = 823.919J, but this is not right...what am i doing wrong?
 
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  • #2
What am i doing wrong with work done by the man? Isn't it just
Wman-Wgrav-Wfriction = 0
Wgrav = -m*g*h
Wfric = -(Coefficient of friction)(m*g)(distance)
 
  • #3
Awwnutz said:
What am i doing wrong with work done by the man? Isn't it just
Wman-Wgrav-Wfriction = 0
Wgrav = -m*g*h
Wfric = -(Coefficient of friction)(m*g)(distance)
The work done by gravity is either -mgh or -mg(sin theta)*d. You used W_grav = -mg(sin theta)*d(sin theta) .

Also, when calculating the friction force, the normal force and the weight are not the same.
 
  • #4
ok so your saying

Wgrav = -(20kg)(9.81m/s^2)(sin33)(1.9m)

And if your turn your coordinate axis so the normal force is going in the positive y direction wouldn't that make the normal force equal and opposite of the weight of the block?
 
  • #5
i figured it out

Wgrav = m*g*(sin theta)*d
Wfric = (Coefficient of friction)*(m*g*cos theta)*d

after that it was quite easy to figure out the rest.

Thanks PhanthomJay!
 

FAQ: Block, Ramp, Friction, and Spring work done

What is the definition of work done in relation to block, ramp, friction, and spring?

Work done is the measure of energy transferred when a force is applied to move an object over a distance. In the context of block, ramp, friction, and spring, it refers to the amount of energy needed to overcome friction and move the block up or down the ramp, compress or stretch the spring, or maintain its position against the force of gravity.

What is the role of friction in determining work done for a block on a ramp?

Friction plays a significant role in determining the work done for a block on a ramp. Friction is the force that opposes the motion of the block, and it is responsible for dissipating the energy put into the system. This means that a higher amount of work is required to move the block up the ramp because some of the energy is lost due to friction.

How does the angle of the ramp affect the amount of work done for a block?

The angle of the ramp directly affects the amount of work done for a block. As the angle of the ramp increases, the distance the block needs to travel to reach a certain height decreases, meaning less work is required. However, a steeper ramp also means a higher force is needed to overcome the increased gravitational force, resulting in more work being done.

What happens to the work done when a spring is compressed or stretched?

When a spring is compressed or stretched, work is done to store potential energy in the spring. This potential energy can then be released as kinetic energy when the spring is allowed to return to its original position. The amount of work done on the spring is directly proportional to the amount of compression or stretching it undergoes.

How do the forces acting on a block affect the work done?

The forces acting on a block, such as gravity, friction, and the force of the spring, all play a role in determining the amount of work done. The work done is equal to the force applied multiplied by the distance the block travels in the direction of the force. Therefore, a higher force or longer distance will result in more work being done.

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