Exam 1. City Tech, Spring 2017. Problems 6,7,8,9,10

11. The motion of some object is described by the two equations
x = 17.7m∙ cos(t/5s),
y = 17.7m∙ sin(t/5s),
z = 0.
What is the magnitude of the acceleration of this object for the time t=3 s?

12. Let two special objects with equivalent masses attract each other by gravity attraction with the force of 5N. What will be gravity attraction of this two objects if mass of one object is increased 2 times, mass another object is increased 18 times, and the distance between objects is increased 6 times?

13. The maximum speed with which a 1200-kg car can round a turn of radius 80 m on an iced float road without slipping is 32.2 km/h. Find the static friction coefficient between tires and road. Use g=10 m/s².

14. What is maximum possible magnitude of the acceleration of the box shown in the picture? The coefficient of the kinetic friction between the box and the inclined surface is 0.1, the inclined surface angle is 30 degrees, the mass of the box is 10 kg. The inclined surface can not move.







15. Two cars start moving simultaneously from opposite ends of a road. If cars are moving with the equal constant speeds, cars meet each other after the time t₁ from the moment of the start. Find the meeting time if the speed of one car would be twice greater but the speed of another car would be twice less.

16. The velocity of a linear motion is given as a function of the x coordinate: v(x)=C/x, where C is the given constant. Find elapsed time to the motion from the known initial position x₀ to the known final position x₁.

Exam 1. City Tech, Spring 2017. The First 10 Problems

Exam 1. City Tech, Spring 2017

1. Two masses, m₁ and m₂ hang over a friction less pulley by means of a mass-less string. They are perfectly balanced when a flea of mass m₃ is standing on m₂. When the flea is standing on m₁, the system has an acceleration a. What are masses m₁ and m₂ in terms of flea's mass m₃ and the acceleration a?

2. The acceleration of masses of an idealized Atwood's machine is a. Find acceleration if the greater mass is increased twice. Neglect friction and the mass of the cord and the pulley.

3. What is the acceleration a in terms of m, M, and g?

4. A body, freely falling from rest, passes the first P% of the total fall distance at the t second. What is the total falling height?

5. The same net force accelerates three object taken separately with the accelerations a1, a2, a3. Find the acceleration, if this net force is acting on these three objects, which are coupled together as one whole.

6. On an inclined plane, an object is moving without the friction under the influence of only the gravity. The object marks positions on the surface through equal intervals of the time. These marks have coordinates L₁, L₂, L₃, L₄ on an axis in the order of appearance. The axis directed along the inclined surface. The origin of this axis is arbitrary. Find the position of the fourth mark L₄ in terms of the three previous L₁, L₂, L₃.

7. If for a moving object the total distance was 3.33 m and total time of the motion was 11.1 s what was the average speed. Write out the final answer with the right number of significant figures.

8. The force F₁ is point out to the x direction and has magnitude of 3 N. The force F₂ is point out to the y direction and has magnitude of 4 N. Write out the vector sum F = F₁ + F₂, using symbols of the unit vectors directed by x, y, and z axes ( i, j, and k with the “roofs”)

9. For some object the equation of linear motion looks like x = 3m+2m/s∙t + 6m/s²∙t². What is the acceleration of this object for the time t=3 s?

1o. For some object the equation of linear motion looks like

x = (3m/s)∙t+(2m/s²)∙t² + (6m/s³)∙t³.

What is the acceleration of this object for the time t=3 s?