# How Do Newton's Laws Apply to a Lemon Half on a Frictionless Surface?

• iamkristing
In summary, a figure shows an overhead view of a lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force F1 has a magnitude of 4.70 N (in the negative x and positive y direction) and is at θ 1 = 29°. Force F2 has a magnitude of 7.00 N (in the positive x and negative y direction) and is at θ 2 = 29°. The lemon half has mass 0.0200 kg.
iamkristing
1. A figure shows an overhead view of a lemon half and two of the three horizontal forces that act on it as it is on a frictionless table. Force F1 has a magnitude of 4.70 N (in the negative x and positive y direction) and is at θ 1 = 29°. Force F2 has a magnitude of 7.00 N (in the positive x and negative y direction) and is at θ 2 = 29°. The lemon half has mass 0.0200 kg.

(a) What is the third force if the lemon half has zero velocity?

(b) What is the third force if the lemon half has constant velocity? v = (13.0 - 14.0 ) m/s

(c) What is the third force if the lemon half has a varying velocity? v = (13.0t - 14.0t ) m/s, where t is time in seconds

2. F= m*a

3. I divided the two forces into x and y components. I then added them together and found the x and y component needed for the lemon not to move. I'm not sure how to use these components to find velocity though.

Also, is there a difference between constant and varying velocity for this problem?

You need to show some working or an attempt before someone helps you.

sorry I have attempted.

I found the x and y components of the first force to be x= -4.11 and y=2.28 and the second force to be y= -3.39 and x=6.12

for the lemon not to move, I found that the third force's x and y components were equal to x=-2.11 and y=1.11

now I did the same except when solving for the third force i set each component equal to the constant velocity. I got x=10.99 and y=-12.89

for the varying velocity question, I know the derivative of velocity is acceleration. So i found the derivative of that function and then applied F=ma. I got x=0.26 abd y=-0.28

Now none of these answers are right and I can't see where I'm going wrong...

I just tried the problem again, taking into account the velocity and acceleration. I thought I missed that before.

So I used the sum of the forces = mass*acceleration

I thought, with zero velocity, no other force would be needed because the velocity doesn't change.

Also, for constant velocity, I found the third force vector needed. I found that to be x=-2.01 and y=1.12

Now for varying velocity, I took the derivative of the velocity the problem gave me. I found the acceleration to be 13 in the x direction and 14 in the y direction. I used F=ma and plugged in the mass of the lemon and the acceleration and got:

F in x direction = 2.27
F in y direction = -0.84

Still though, I cannot come up with the answer. Any help or point in the right direction will be helpful!

## 1. What are Newton's laws on a lemon half?

Newton's laws on a lemon half refer to the application of Newton's three laws of motion to a lemon half. These laws describe the relationship between an object's motion and the forces acting upon it.

## 2. What is Newton's first law on a lemon half?

Newton's first law, also known as the law of inertia, states that an object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by an external force. In the case of a lemon half, this means that if it is not moving, it will remain still, and if it is moving, it will continue to move in the same direction and at the same speed unless acted upon by a force.

## 3. How does Newton's second law apply to a lemon half?

Newton's second law states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. This means that the greater the force applied to a lemon half, the greater its acceleration will be. Similarly, the more massive the lemon half is, the less it will accelerate for a given amount of force.

## 4. What is the significance of Newton's third law on a lemon half?

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when a force is applied to a lemon half, it will exert an equal force in the opposite direction. This can be seen when squeezing a lemon half, as the force applied to the lemon will result in an equal force pushing back on your hand.

## 5. How do Newton's laws on a lemon half relate to everyday life?

Newton's laws on a lemon half may seem like a simple concept, but they have significant applications in everyday life. For example, when throwing a lemon half, the force applied to it will determine how far it will travel. Additionally, these laws can also be applied to more complex systems, such as the motion of objects in space or the movement of vehicles on the road.

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