How Do You Calculate Forces on Inclined Planes?

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In summary: When the crate is moving at a constant velocity, the sum of the forces in the x-direction and y-direction must be equal to zero. In summary, the given problems involve finding the tension in a cord, normal force, and acceleration of a block on an inclined ramp, as well as the normal force and horizontal force on a crate on a frictionless ramp. The tension in the cord is found using the mass of the block and the angle of the ramp, while the normal force is determined using the weight of the block and the angle of the ramp. For the second problem, both the horizontal force and the normal force must be considered in order to determine the crate's constant velocity.
  • #1
jarny
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Homework Statement



I have two questions:

1. Let the mass of the block be 8.2 kg and the angle θ be 37°. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration.

2.In the figure, a crate of mass m = 104 kg is pushed at a constant speed up a frictionless ramp (θ = 29°) by a horizontal force f-> . The positive direction of an x-axis is up the ramp, and the positive direction of a y-axis is perpendicular to the ramp. (a) What is the magnitude of f-> ? (b) What is the magnitude of the normal force on the crate?



Homework Equations



F_net=ma
Maybe T-m*g*sin(theta)=ma


The Attempt at a Solution



Ok, for 1.a. I used 8.2kg*9.8m/s^2*cos(29)=48.3619N to find the tension on the cord. For b I used 8.2*9.8*sin(29)=64.1783N. For 3. I am having trouble because my T and mgsintheta are the same.

For 2a. I used 104kg*9.8m/s^2tan(29) to get 564.92N and for B is got 1019N*cos(29) but the computer says this is wrong. The only one I got right was 2.a, 1.a and 1.b were revised so they might be right.



Can anyone help? Thank you very much
 
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  • #2
Welcome to PF.

What is the diagram of the problems you are solving.
 
  • #3
Last edited:
  • #4
1)The force component of gravity pointing down the ramp is sinθ.

Hence the Tension to off set that in the direction up the ramp is m*g*sinθ = m*a where a is the answer to your part c.

The Cosθ component of g determines the force normal to the incline.

2) For part b you have two components of force to account for.

From the F you have F*sinθ
From mass and gravity you have m*g*Cosθ
 

1. What is the purpose of studying "Boxes on Ramps (forces)"?

The purpose of studying "Boxes on Ramps (forces)" is to understand the principles of mechanics and how forces act on objects on inclined planes. This knowledge is crucial for designing and building structures, machines, and other systems that involve the use of inclined planes.

2. How does the weight of the box affect its motion on the ramp?

The weight of the box affects its motion on the ramp because it is the force of gravity acting on the box. The steeper the ramp, the greater the force of gravity and the faster the box will accelerate down the ramp. On the other hand, a shallower ramp will result in a smaller force of gravity and a slower acceleration.

3. What is the relationship between the angle of inclination and the force required to move the box up the ramp?

The relationship between the angle of inclination and the force required to move the box up the ramp is directly proportional. As the angle of inclination increases, the force required to move the box up the ramp also increases. This is because a steeper ramp results in a greater component of the weight of the box acting against the direction of motion.

4. How does friction affect the motion of the box on the ramp?

Friction plays a significant role in the motion of the box on the ramp. It acts in the opposite direction of the motion and can either assist or hinder the motion depending on the direction of the force. If the force pushing the box up the ramp is greater than the force of friction, the box will accelerate up the ramp. However, if the force of friction is greater than the force pushing the box, it will slow down or even come to a stop.

5. How do you calculate the net force on the box on the ramp?

To calculate the net force on the box on the ramp, you need to consider all the forces acting on the box, including the force of gravity, normal force, and friction. The net force can be found by taking the difference between the force pushing the box up the ramp and the force of friction acting against it. If the net force is positive, the box will accelerate up the ramp, and if it is negative, the box will decelerate or move in the opposite direction.

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