A steel ball has a mass of 4.0kg and rolls along a smooth, level surface at 62m/s.
A) Find its kinetic energy(i got this and its 7688 joules)
B)?????-At first, the ball was at rest on the surface. A constant force acted on it through a distance of 22 meters to give it the speed of 62m/s. What was the magnitude of the force??
I really don't understand part b. please help in detail! Thxs
Use V(final)^2=V(initial)^2+2ad
62^2 = 0 + 2(a)(22)
a=87.364 m/s^2
Then use F=ma
F=(4)(87.364)
F=349.455 N (you may have to round this to get 2 sig figs)
B) Ah, the magnitude of the force question, always raising eyebrows. Here's the lowdown: to find the magnitude of the force, we need to understand that work is done on an object when a force acts on it and moves it through a certain distance.
In this case, the work done on the ball is equal to the change in its kinetic energy. We can calculate the work done using the equation:
Work = Force x Distance
Since we know the distance (22 meters) and the kinetic energy (7688 joules, as you kindly mentioned), we can plug those values in:
7688 joules = Force x 22 meters
Now we just need to solve for the force. Dividing both sides of the equation by 22 meters, we get:
Force = 7688 joules / 22 meters
And voila! The magnitude of the force is equal to the work done divided by the distance traveled. Plug in those numbers and you'll get your answer.
Hope that clarifies things for you!
Sure! I can help you understand part B.
To find the magnitude of the force, we can use the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy.
In this case, the work done on the ball is equal to the force applied multiplied by the distance over which the force is applied. Since the force is constant, we can write:
Work = Force * Distance
The work done on the ball is also equal to the change in its kinetic energy. We know the initial kinetic energy is zero (since it was initially at rest) and the final kinetic energy is 7688 joules (which you found in part A).
Therefore, we can write:
Work = Change in Kinetic Energy
Substituting the values, we get:
Force * Distance = 7688 joules
The distance over which the force is applied is given as 22 meters. Therefore, we can solve for the magnitude of the force:
Force = 7688 joules / 22 meters
Calculating this, we find that the magnitude of the force is approximately 349.45 Newtons.
So, the magnitude of the force required to give the steel ball a speed of 62 m/s over a distance of 22 meters is approximately 349.45 Newtons.
Sure! I can help you with part B.
To find the magnitude of the force, we can use the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
In this case, the work done on the steel ball is equal to the force acting on it multiplied by the distance it moves. The work done on the ball causes its kinetic energy to increase from 0 to the final value of 7688 joules.
So, mathematically, we can represent this as:
Work = Force × Distance
Change in kinetic energy = Final kinetic energy - Initial kinetic energy
Since the ball starts from rest, its initial kinetic energy is 0.
Therefore, we have:
Work = Force × Distance = Change in kinetic energy
Plugging in the given values:
Distance = 22 meters
Change in kinetic energy = 7688 joules
Now, we can rearrange the equation to solve for the force:
Force = Work / Distance
Force = Change in kinetic energy / Distance
Force = 7688 joules / 22 meters
Calculating the force:
Force = 349.45 Newtons
So, the magnitude of the force acting on the steel ball was approximately 349.45 Newtons.