Assignment help needed. (banked curves, Newton's second law)

[serenite]

I was solving my assignment questions, and found two questions particularly challenging.
So I post this thread to get some helps.

1. Homework Statement
Question 1.

Astronauts have connected a line between their 3500kg space tug and a 6200 kg asteroid. Using their ship's engine, they pull on the asteroid with a force of 490 N. They are at rest, 450 m apart. How much time does it take for them to meet?

3. The Attempt at a Solution
At first glance, I thought that net force is 490N, and can never be stronger. Thus I concluded that this can be simplified such that the space tug is completely still and the asteroid is moving towards the tug with (490/9700)m/s^2. But I'm not so sure about this. In fact I think it's probably wrong. Should I distribute the force to each objects by their percent mass?

1. Homework Statement
Question 2.
A suitcase is on a baggage carousel at an airport. The case does not slid and is going around at a constant speed on a circle (r=11,0). The static friction is 0.760 and the angle is 36.
How much time is required for the suit case to go around once?

3. The Attempt at a Solution
For this one, I don't even know where to start. I used the equation g*r*tan (theta). After that, I was not able to go any further.

Thanks.

 

[jbsteele]

For the first question, you can use Newton's Second Law of Motion to calculate the acceleration of the space tug and asteroid. The equation is F = ma, where F is the force acting on the objects, m is their mass, and a is the acceleration. So, in this case, the acceleration of the tug and asteroid would be 490N/3500kg for the tug and 490N/6200kg for the asteroid. Once you have the accelerations of each object, you can use kinematics equations to determine the time it will take them to meet. The equation you will need is x = v0t + 1/2at^2, where x is the distance between the objects, v0 is the initial velocity of the objects (which is 0 in this case), a is the acceleration, and t is the time it takes for the objects to meet. For the second question, you can use the equation v = (g*r*tan(theta))/f, where v is the velocity of the suitcase, g is the gravitational acceleration (9.8m/s^2), r is the radius of the circle, theta is the angle, and f is the static friction. This equation will give you the velocity of the suitcase. Once you have the velocity, you can use the equation t = 2*pi*r/v, where t is the time it takes for the suitcase to go around once, pi is 3.14, and r is the radius of the circle.

 

[tomcue]

Dear student,

Thank you for reaching out for help with your assignment. It seems like you are struggling with two questions related to banked curves and Newton's second law. I will try my best to provide some guidance and clarification.

For question 1, you are correct in thinking that the net force is 490N. However, to solve for the time it takes for the astronauts to meet, we need to consider the acceleration of the objects. Since the tug and asteroid are connected, they will have the same acceleration. We can use Newton's second law, F=ma, to find the acceleration of the system. The total mass of the system is 3500kg + 6200kg = 9700kg. So, the acceleration will be 490N/9700kg = 0.05m/s^2. From here, you can use the equation s=ut+1/2at^2 to solve for time, where u is the initial velocity, which is 0 since they are at rest. The distance, s, is 450m and the acceleration is 0.05m/s^2. Solving for t, we get t=30 seconds. So, it will take 30 seconds for the astronauts to meet.

For question 2, the key is to understand the forces acting on the suitcase. The only horizontal force acting on the suitcase is the static friction, which is equal to the centripetal force. We can use the equation F=m*v^2/r to solve for the velocity. The mass of the suitcase is not given, so we can use the given static friction and angle to find the coefficient of friction, which is 0.760. The equation becomes 0.760*m*9.8 = m*v^2/11. Solving for v, we get v=2.2m/s. Now, we can use the equation v=2*pi*r/t to solve for time. Plugging in the values, we get t=5.3 seconds.

I hope this helps you to understand the concepts and solve the questions. Remember to always consider the forces and acceleration when solving problems related to Newton's second law. Best of luck with your assignment!