Unit 4 Summary: Unbalanced Force Particle Model
Newton's Second Law:
I drew the quantitative free body diagram and than proceeded with calculating the acceleration. As you can see, it was a multi-step process. First, I had to calculate the Friction (Ff = Mk * Fg) which was 15 Newtons. I than had to calculate the ΣF, which was -5 Newtons. The final step was to calculate the acceleration (a = ΣF/m), which was .33 m/s2.
3.
Michael and Angela are riding the elevator up to the 95th floor of the building. The elevator is traveling up at a constant velocity of 17 m/s. Michael and Angela have a combined mass of 130 kilograms. Construct a force diagram for the situation and than calculate the force the floor exerts on the passengers.
The skier is traveling down an inclined slope which measures 30 degrees. When drawing the free body diagram for problems involving inclined slopes, always place the given between the Fg and Fgy. The Fgx equals the ΣF, so once I solved for the ΣF using Cos(60) = Fgx/750 = (750)(Cos60) = 375, I had also calculated the Fnet. To calculate for the acceleration, I plugged in the known variables into the a = ΣF/m formula (a = 375/75). 375 divided by 75 equals 5, so the acceleration is 5 m/s2.
Conclusion:
In this unit, I learned about Newton's Second Law of Motion and the Unbalanced Force Particle Model. Newton's Second law says that the force acting on an object is equal to the mass of that object times its acceleration. I also learned that acceleration t is directly proportional to the net force, but is inversely proportional to mass. I learned that the net force is the sum of all the forces acting upon an object and that the direction of the acceleration is in the direction of the net force acting on the object. Unbalanced forces must act upon an object in order to accelerate and an object at rest is being acted upon by balanced forces. In this unit, I began to use the kinematic equations in order to calculate for the unknowns. When dealing with the motion of elevators, I learned that when an object is speeding up, the acceleration is in the same direction as the velocity. However, when the acceleration and velocity are in opposite directions, the object is slowing down.
Sources Cited:
http://images.hellokids.com/_uploads/_tiny_galerie/20100102/bobsled-source_ckr.jpg
https://www.sixflags.com/sites/default/files/kingda_ka_3.jpg
In this unit, I learned about Newton's Second Law of Motion and applied it to a multitude of scenarios. I also learned about unbalanced forces and how to calculate the net force acting on an object.
Newton's Second Law:
- The second law says that the force acting on an object is equal to the mass of that object times its acceleration.
- This is represented by the formula: F = ma (ΣF = m*a)
- F is force, m is mass and a is acceleration.
- The acceleration of an object is directly proportional to the net force acting on it, and is inversely proportional to its mass.
- The direction of the acceleration is in the direction of the net force acting on the object.
- So, the net force is the sum of all the forces acting on an object. A net force is capable of accelerating a mass.
The bobsled accelerates because the team exerts a force.
Friction and Coefficients of Friction
- Ff = Mk * Fg
- Ff = frictional force (N)M (Mu) = frictional coefficientFg = Weight of object
Units and Equations for this Model:Vf - Final VelocityV0 - Initial Velocitya - Accelerationt - TimeΔx - Δ is displacement
x0 - Starting (initial) position
In this model, we began to apply the kinematic equations to scenarios in order to calculate unknown variables.
Concept Practice:
1. Above is a modified Atwood Machine, we can calculate the net force on the system using the hanging block's mass. Let's say the hanging block's mass is 100g.
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| I drew the free body diagram and calculated the net force on the system.
2.
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| Above is a person pushing a 15 kg box with 20 N to the left. The positive direction is the right and the coefficient of friction between the surfaces is .11. What is the acceleration of the box? |
3.
Michael and Angela are riding the elevator up to the 95th floor of the building. The elevator is traveling up at a constant velocity of 17 m/s. Michael and Angela have a combined mass of 130 kilograms. Construct a force diagram for the situation and than calculate the force the floor exerts on the passengers.
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| Since the elevator was traveling at constant velocity, it is quite easy to calculate the force exerted by the floor (or the ΣF). The acceleration is force of Earth's gravity and and the mass is 130 kilograms (or 1300 N). By knowing the mass and the acceleration, I can calculate the ΣF. Which the ΣF equals 12,740 Newtons. 3b. The same elevator soon begins to accelerate upward at 4 m/s2. Now what is the force exerted by the floor on the passengers?
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5.
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| The rollercoaster, Kingda Ka, is the world's tallest rollercoaster at a height of 139 meters (456 feet). As the passenger cars are launched from rest at the start they accelerate uniformly to a speed of 57 m/s (128 mph) in just 3.5s. While accelerating, friction exerts 450N on the train. Loaded with passengers, the train has a mass of 8325 kg. Calculate for all the unknowns. |
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| The train goes from rest to 57 m/s in just 3.5 seconds. With this information, I calculated the acceleration using the a = Δv/t (a = 57 - 0/3.5) formula, which equals around 16.2 m/s2. Once I calculated the acceleration I could now calculate for the Δx using Δx = Vit + .5at2 (Δx = 0*3.5 + .5*16.2*3.52). I calculated the Δx to be 85.85 meters. I than calculated the ΣF using a = ΣF/m (16.2 = ΣF/8,325). I calculated the ΣF to be 135,865 Newtons. Once I had calculated the ΣF, I could calculate the Fpush using the ΣF = Fpush + FF (134,864 = Fpush - 450). I collocated the Fpush to be 135,315 Newtons. |
Conclusion:
In this unit, I learned about Newton's Second Law of Motion and the Unbalanced Force Particle Model. Newton's Second law says that the force acting on an object is equal to the mass of that object times its acceleration. I also learned that acceleration t is directly proportional to the net force, but is inversely proportional to mass. I learned that the net force is the sum of all the forces acting upon an object and that the direction of the acceleration is in the direction of the net force acting on the object. Unbalanced forces must act upon an object in order to accelerate and an object at rest is being acted upon by balanced forces. In this unit, I began to use the kinematic equations in order to calculate for the unknowns. When dealing with the motion of elevators, I learned that when an object is speeding up, the acceleration is in the same direction as the velocity. However, when the acceleration and velocity are in opposite directions, the object is slowing down.
Sources Cited:
http://images.hellokids.com/_uploads/_tiny_galerie/20100102/bobsled-source_ckr.jpg
http://s3.amazonaws.com/siteninja/site-ninja1-com/1404085954/large/pushing_heavy_box_10368-300x196.png
http://4.bp.blogspot.com/-fkjH9mBEgTw/UEHQCVSTAvI/AAAAAAAAABo/ohNDu_TB90Q/s1600/notfreefall.jpg
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