Kara (55kg) is standing next to her brother Ben (80kg) on a large piece on frictionless ice. Kara decided to push her brother with a force of 200N expecting him to slide across the ice while she remains standing in the middle of the ice rink laughing.
a) Describe the motion that will actually be experienced by Kara and Ben. Use the appropriate vocabulary to describe the motion. Describe the motion from beginning, middle and end
This is what I think but it may not be correct. In the beginning, Kara and Ben are on the ice and as Kara tries to push Ben she ends up sliding across the ice since she weighs less and because the surface is frictionless while Ben moves slightly. In the middle, Kara would be moving away from Ben at a faster rate than Ben is moving. In the end, Ben would stop moving first and Kara would follow after. They would come to a stop because of air resistance. (I'm not sure what type of motion vocabulary I am to be using).
b) What is Ben's acceleration and Kara's acceleration?
Would Ben's acceleration be 2.5m/s^2 and Kara's be 3.6m/s^2?
Since there is no external force on the system at the beginning (air and ice friction is later), the momentum of the center of mass will not move
That means:
Mass ben * Vben + mass kara * Vkara = 0
V kara = - V ben (Mass ben / Mass kara)
so at all times Kara's speed is greater than Ben's speed but in the opposite direction. Chances are she would drift further before stopped by friction
F = 200 call it + on Ben and - on Kara
a = F/m
a ben = 200/ 80
a kara = -200/ 55
a) Well, Kara's plan might sound amusing, but the actual motion would be quite different. Because of Newton's Third Law, for every action, there is an equal and opposite reaction. When Kara pushes Ben with a force of 200N, an equal force is exerted on her in the opposite direction. As a result, Kara and Ben would both slide in the same direction, away from each other. Neither of them would remain stationary. The motion experienced by Kara and Ben would be uniform motion, in which they both slide with constant velocity due to the absence of any external forces (except for air resistance).
In the beginning, Kara pushes Ben with a force of 200N, causing them both to slide across the ice in opposite directions. In the middle, they continue to slide at a constant speed away from each other. In the end, they would gradually slow down and come to a stop due to the opposing force of air resistance.
b) Ben's acceleration and Kara's acceleration would actually be zero. Since the ice is frictionless and there are no external forces acting on them (except for air resistance), they will slide with a constant velocity, which means there is no change in their acceleration. So, Ben's acceleration and Kara's acceleration would both be zero.
a) The motion that will actually be experienced by Kara and Ben can be described as follows:
In the beginning, Kara and Ben are both stationary on the frictionless ice. When Kara pushes Ben with a force of 200N, an equal and opposite force (due to Newton's third law) acts on Kara. As a result, Kara and Ben both start moving in the opposite direction to the applied force.
In the middle, Kara and Ben will experience different motions. Due to her lower mass, Kara will accelerate away from Ben at a faster rate. She will continue to slide across the ice at a constant speed due to the absence of friction, until acted upon by an external force like air resistance.
On the other hand, Ben, with a higher mass, will begin to move but at a slower rate compared to Kara. He will experience a smaller acceleration and will eventually come to a stop when the applied force is no longer present.
In the end, both Kara and Ben will eventually come to a stop due to the presence of air resistance, which acts against their motion.
b) To calculate the accelerations of Kara and Ben, we need the masses of Kara and Ben, and the net force acting on each of them.
Given that Kara's mass is 55kg and Ben's mass is 80kg, and the force applied by Kara is 200N, we can calculate the accelerations using Newton's second law, which states that force equals mass multiplied by acceleration (F=ma).
For Kara:
Force (F) = 200N
Mass (m) = 55kg
Rearranging the formula, we get:
Acceleration (a) = Force / Mass
Acceleration (a) = 200N / 55kg
Acceleration (a) ≈ 3.64 m/s^2 (rounded to two decimal places)
For Ben:
Force (F) = -200N (opposite direction compared to Kara's force)
Mass (m) = 80kg
Acceleration (a) = Force / Mass
Acceleration (a) = -200N / 80kg
Acceleration (a) ≈ -2.5 m/s^2 (rounded to two decimal places)
So, Ben's acceleration would be approximately -2.5 m/s^2, and Kara's acceleration would be approximately 3.64 m/s^2.
a) The motion experienced by Kara and Ben can be described as follows:
Beginning: Both Kara and Ben are initially at rest on the frictionless ice. Kara applies a force of 200N to push Ben.
Middle: As Kara pushes Ben, an equal and opposite reaction force will act on Kara due to Newton's third law of motion. Since Kara weighs less than Ben, the force she exerts will cause her to move away from Ben at a faster rate than Ben moves. Therefore, Kara will start sliding across the ice in one direction, while Ben will also start moving but at a slower rate in the opposite direction.
End: Eventually, both Kara and Ben will come to a stop due to external factors such as air resistance and any collisions they might experience with other objects. Kara will stop sliding first, since her lower weight and potentially higher velocity result in a quicker deceleration. Ben, being heavier, will take longer to come to a stop.
b) To calculate the acceleration of an object, you need to know the mass of the object and the net force acting on it. In this scenario, the net force acting on both Kara and Ben is the force applied by Kara, which is 200N.
Using the formula F = ma, where F is the force, m is the mass, and a is the acceleration, we can rearrange the formula to solve for acceleration:
a = F / m
For Ben:
Mass (m) = 80 kg
Force (F) = 200 N
a = 200 N / 80 kg
a = 2.5 m/s^2
For Kara:
Mass (m) = 55 kg
Force (F) = 200 N
a = 200 N / 55 kg
a ≈ 3.64 m/s^2 (rounded to two decimal places)
Therefore, Ben's acceleration would be approximately 2.5 m/s^2, and Kara's acceleration would be approximately 3.64 m/s^2.