Vectors, Forces Accelerating a Train

[blackcannon]

If anyone could help me with these two questions that would be great.

1.A freight train has a mass of 1.20E+7 kg. If the locomotive can exert a constant pull of 8.03E+5 N, how long does it take to increase the speed of the train from rest to 70.6 km/hr?

2.A football punter kicks a football from rest so that it attains a speed of 14.0 m/s during the time in which his toe is in contact with the ball (about 0.29 s). If the football has a mass of 0.520 kg, what average force (in N) does the punter exert on the ball?

 

[BAnders1]

It still disgusts me how a lot of physics textbooks make students do numerical calculations instead of general solutions. That aside...

Both questions are talking about a CHANGE IN VELOCITY. What is the change in velocity called? Hint: It's called acceleration, shhhh don't tell.

For question 1:
If you accelerate at a constant rate for some time, what is your velocity (that is, how does velocity depend of time, given that acceleration is constant? Your textbook most likely answers this, look up "kinematic equations" if you can't find it.) After figuring this out, ask yourself how force, mass, and acceleration are related, Mr. Newton.

For question 2:
The basic idea of the question is the same as question one, except now you know the time, velocity, and force, instead of the force, mass, and velocity. Just think of how the four variables (F, m, a, v) are related.

I hope this helps you. If you have any further questions with this or other problems, feel free to post or PM them.

 

[tomcue]

I would approach these questions by first identifying the relevant physical principles and equations that can be applied to solve them. In the first question, we are dealing with the concept of force and acceleration, which can be described by Newton's Second Law of Motion, F=ma. We also need to consider the initial and final velocities of the train, as well as the time it takes to reach the final velocity.

To solve for the time, we can rearrange the equation F=ma to solve for time, t=mv/F. Plugging in the given values, we get t=(1.20E+7 kg)(70.6 km/hr)/(8.03E+5 N)= 1.05 hours. Therefore, it would take the train 1.05 hours to reach a speed of 70.6 km/hr.

In the second question, we are dealing with the concept of impulse, which is the change in momentum of an object. We can use the equation impulse=force x time, or J=FΔt, to solve for the average force exerted by the punter. We are given the mass, initial and final velocities, and the time of contact between the ball and the punter's foot.

Plugging in the values, we get J=(0.520 kg)(14.0 m/s)= F(0.29 s). Solving for F, we get F= 24.9 N. Therefore, the average force exerted by the punter on the ball is 24.9 N.

In both cases, it is important to consider the direction of the force and the acceleration of the objects. Vectors play a crucial role in understanding and solving problems involving forces and accelerations. It is also important to note that these calculations are based on ideal conditions and may vary in real-life situations due to factors such as friction and air resistance.