Classical Mechanics Answers

A sailor in a small sail boat encounter shifting winds. She sails 2.00km East , then 3.50km 45° Southeast, and then an additional distance in an unknown direction

A particle and a frame, both rotate about a common axis with the same angular velocity as observed from the lab frame (inertial). The particle is not on the axis of rotation. As seen from the rotating frame,

(a) Centrifugal force is zero but Coriolis force is nonzero

(b) Centrifugal force is nonzero but Coriolis force is zero

(c) Centrifugal force and Coriolis force are both zero

(d) Centrifugal force and Coriolis force are both nonzero

Particles A and B exert forces on each other which are attractive in nature and the magnitude depends only on the separation between them. The masses of A and B are M and 8M. To get the motion of A with respect to B, one has to use reduced mass M_A and to get the motion of B with respect to A, one has to use the reduced mass M_B.

(a) M_A> M_B

(b) M_A <M_B

(c) M_A = M_B

(d) M_A < M

(e) M_A < 8M

A particle moves under a central force field. The quantity  [d²/dθ² (1/r)]  is proportional to 1/r. The symbols have standard meaning. The magnitude of the force is proportional to

(a) 1/r²

(b) 1/r

(c) 1/ r³

(d) r

(e) none of these

Consider a particle moving in a central force field 

f(u) = - ku³

using standard notations u = 1/r. The quantity

d²u/dθ² + u

(a) is proportional to u²

(b) is proportional to u

(c) is a constant

(d) is proportional to 1/u

(e) none of these

Consider a particle moving in a central force field

           f(u) = - ku²

using standard notation u =1/r. The quantity 

d²u/dθ² + u

(a) is proportional to u²

(b) is proportional to u

(c) is a constant

(d) is proportional to 1/u

(e) none of these

Assume that (a) the earth is a sphere of radius R with uniform density and (b) the earth exerts only the gravitational force on the object even if the object hits and enters the earth.

(a) The total energy remains the same in the entire motion.

(b) The angular momentum remains the same in the entire motion.

(c) The whole path of the object is elliptical

(d) The motion of the object remains bound

The potential energy of a particle is given by V=V₀ [(a/x)¹² - (b/x)⁶ ]

(a) The constants a and b are dimensionless

(b) The constants a and b have same dimensions

(c) V versus x graph intersects the x-axis at only one point

(d) V versus x graph has only one minima

 Incline 40 degrees, incline-object = 2 kg, hanger mass = 4 kg

Use 9.8 m/s/s for g

Describe how mu increased, acceleration down, but tension internal force up

Plot tension on y-axis, acceleration on x-axis for the 2 kg mass with mu =0.25 using the 2 kg equation of (T, a). Repeat for the 4 kg using the 4 kg equation of (T, a) on the same graph, the intersection is the graphical solution. Repeat for the 2 kg with mu=0.4 using the 2 kg equation of (T, a) on the same graph, the intersection is the graphical solution.

Writing intensive: explain the graph as a trend justification, the shift of the intersection points to other values.

 Incline 40 degrees, incline-object = 2 kg, hanger mass = 4 kg

Use 9.8 m/s/s for g

Describe how mu increased, acceleration down, but tension internal force up

Plot tension on y-axis, acceleration on x-axis for the 2 kg mass with mu =0.25 using the 2 kg equation of (T, a). Repeat for the 4 kg using the 4 kg equation of (T, a) on the same graph, the intersection is the graphical solution. Repeat for the 2 kg with mu=0.4 using the 2 kg equation of (T, a) on the same graph, the intersection is the graphical solution.

Writing intensive: explain the graph as a trend justification, the shift of the intersection points to other values.

draw the Qx and Mx diagrams for the beam shown in the figure find the maximum bending moment