Calculating Forces and Power on a Block on an Inclined Plane

In summary, the force on the string is 10.4 N when the block is stationary, and 8.8 W when the block is moving at 0.85 m/s up the inclined plane.
  • #1
ProPM
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A block is held stationary on a frictionless inclined plane by means of a string.

The angle of inclination of the plane is 25 degrees, the block has mass 2.6 kg. Calculate the force on the string, you may assume that g = 9.8 m/s2 . Sorry for the poor quality of the attachment but I think you get the idea.

So, its the first time I came across this type of question so I'm not sure whether what I did is correct or not:

a) So the force on the string: Block not moving, thus, equal to parallel component of the weight, hence:

T = sin 25 x (2.6 x 9.8)
T = 10.4 N

b) The string is pulled so that the block is now moving at a constant speed of 0.85 m/s up the inclined plane: Explain why the magnitude of the force on the string is the same now as it was in the first question?

N1 First Law says that if forces are balanced, object must be at rest or moving at a constant velocity, thus, since the weight didn't change, the force on the string must be the same

c) Calculate the power required to move the block at this speed:

P = F x velocity
P = (sin 25) x (9.8 x 2.6) x 0.85
P = 8.8 W

d) State the rate of change of GPE of the block:

So, in 1 second, since moving at 0.85 m/s, block is displaced 0.85 m in one second at an angle of 25. Thus, vertical displacement in one second = sin 25 x 0.85
hence: (mxgxh) = (2.6 x 9.8 x (sin 25 x 0.85)) = 9.15 W

Thanks in advance,
Peter G.
 

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  • #2
Looks good to me.
 
  • #3
Thanks, I was afraid that, when calculating the force on the string, thus, finding the parallel component of weight I had not used the right trig law, since that could alter all my other answers. So I did that right?
 

1. What is a block on an inclined plane?

A block on an inclined plane is a common physics problem that involves a block of mass m resting on a plane that is inclined at an angle θ to the horizontal surface. The block is subject to the force of gravity and may also experience other forces, such as friction, depending on the specific problem.

2. How do you calculate the force of gravity on a block on an inclined plane?

The force of gravity on a block on an inclined plane can be calculated using the equation Fg = mg sinθ, where m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of inclination. This equation takes into account the component of the force of gravity that acts parallel to the inclined plane.

3. What is the normal force on a block on an inclined plane?

The normal force on a block on an inclined plane is the force that the plane exerts on the block perpendicular to its surface. It is equal in magnitude but opposite in direction to the component of the force of gravity that acts perpendicular to the plane. The equation for the normal force is Fn = mg cosθ.

4. How does the angle of inclination affect the motion of a block on an inclined plane?

The angle of inclination affects the motion of a block on an inclined plane by changing the forces acting on the block. As the angle increases, the component of the force of gravity parallel to the plane increases, making it more difficult for the block to slide down. On the other hand, a smaller angle of inclination results in a smaller normal force, making it easier for the block to slide down the plane.

5. What is the relationship between the coefficient of friction and the angle of inclination for a block on an inclined plane?

The coefficient of friction, μ, is a measure of the amount of friction between two surfaces. The relationship between μ and the angle of inclination is that as the angle increases, the component of the force of gravity parallel to the plane also increases, resulting in a larger force of friction acting on the block. Therefore, the coefficient of friction will also increase with the angle of inclination.

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