A 257kg motor cycle and rider accelerate from rest and reach a velocity of 20 meters per second west. The motor cycle wheels exert an average force 710N east of the road.Explain how the force directed east causes the motorcycle to accelerate west
That force East is opposed by Earth. Actually, the motorcycle is starting to increase the speed of rotation of Earth,but is is very massive, and the change in rotation is very, very small. Since the Earth is opposing this motion, it is pushing back on the motorcycle westward, and the motorcycle moves west across the earth. Overall, the momentum changes in Earth Rotation and the motorcycle rotation are equal, keeping the conservation of momentum law intact (total momentum change is zero)
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Well, it's like this. The motorcycle and the rider are in a bit of a disagreement, as they both want to go their separate ways. The motorcycle is all "I want to accelerate west!" while the rider is like "No way, we're going east!"
Now, the motorcycle wheels, being the neutral party in this argument, have to intervene. They exert an average force of 710N eastward on the road. This force causes a reaction from the road, commonly referred to as friction. The road pushes back on the motorcycle with an equal and opposite force.
So, while the force is directed eastward, it actually causes the motorcycle to accelerate westward. This is because of Newton's third law, which states that for every action, there is an equal and opposite reaction. The force exerted by the road pushes the motorcycle and rider in the opposite direction – in this case, westward.
So, to summarize: the force directed eastward creates a reaction force from the road, which in turn causes the motorcycle and rider to accelerate westward. It's a classic case of physics being a bit of a trickster!
To understand how the force directed east causes the motorcycle to accelerate west, we need to apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
In this scenario, the force exerted by the motorcycle wheels on the road is directed east with a magnitude of 710N. According to Newton's third law, the road exerts an equal and opposite force on the motorcycle, which is directed west.
This force exerted by the road on the motorcycle is what allows the motorcycle to accelerate. The force causes the motorcycle and the rider to experience a net force in the westward direction, which results in an acceleration in the same direction.
By Newton's second law of motion (F = ma), the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the mass of the motorcycle and rider is 257kg.
Given that the motorcycle and rider reach a velocity of 20 meters per second west, we know that they were initially at rest. Therefore, the final velocity (vf) is 20 m/s and the initial velocity (vi) is 0 m/s.
Using the equation:
vf^2 = vi^2 + 2aΔx
where Δx is the displacement, we can rearrange the equation to solve for acceleration (a):
a = (vf^2 - vi^2) / (2Δx)
Since the motorcycle started from rest, the initial velocity (vi) is 0 m/s. Substituting the values:
a = (20^2 - 0^2) / (2Δx)
a = 400 / (2Δx)
a = 200 / Δx
Now, we can relate the force (F) to the acceleration (a) using Newton's second law:
F = ma
We know that the mass (m) is 257kg, and the force (F) is 710N. Substituting these values:
710N = 257kg * a
By rearranging the equation, we can solve for acceleration (a):
a = 710N / 257kg
a ≈ 2.77 m/s^2
Now, we can substitute this value of acceleration back into the previous equation:
a = 200 / Δx
Rearranging the equation to solve for Δx:
Δx = 200 / a
Δx = 200 / 2.77
Δx ≈ 72.12 m
Therefore, the displacement of the motorcycle during the acceleration is approximately 72.12 meters westward.
In conclusion, when the motorcycle exerts a force directed east on the road, the road exerts an equal and opposite force directed west on the motorcycle. This force causes the motorcycle to experience a net force in the westward direction, leading to an acceleration in the same direction.
To explain how the force directed east causes the motorcycle to accelerate west, we need to understand Newton's third law of motion which states that for every action, there is an equal and opposite reaction.
In this scenario, the eastward force exerted by the motorcycle wheels on the road is the action, and the reaction is the westward force applied by the road on the motorcycle.
When the motorcycle is at rest, the forces acting on it are balanced, resulting in zero net force. However, once the motorcycle starts accelerating, the eastward force exerted by the wheels becomes the unbalanced force that overcomes the inertia of the motorcycle-rider system.
As a result of Newton's third law, the reaction force applied by the road on the motorcycle is equal in magnitude but opposite in direction. This reaction force is the westward force that causes the motorcycle to accelerate.
According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The formula for this relationship is:
acceleration = net force / mass
In our scenario, the net force acting on the motorcycle is the eastward force exerted by the wheels:
net force = 710 N
The mass of the motorcycle-rider system is:
mass = 257 kg
Therefore, the acceleration of the motorcycle can be calculated as:
acceleration = 710 N / 257 kg = 2.77 m/s²
Since the acceleration is occurring in the opposite direction of the applied force (westward), the force directed east causes the motorcycle to accelerate west.
So, in summary, the eastward force exerted by the motorcycle wheels on the road causes an equal and opposite westward reaction force by the road on the motorcycle. This reaction force, in accordance with Newton's second law, results in the westward acceleration of the motorcycle.