7/26/2019 Mechanics Test 3

1/2

PHYSICS MECHANICS

Test 3

SCAN 1st

Exercise 1:

A smooth sphereAof mass m travelling in plane ( ), ,O x y

with velocity

( ) 0*V O v x=

hits a similar sphereBat rest such that the angle between the line of centres

and axis ( ),B y

is (Figure 1). Friction is neglected.

1) Assuming that the coefficient of restitution is e , find the velocities of A and B

after impact.

2) Calculate the energy loss during the impact.

3) SphereBthen hits a wall at a distancedfrom O. The impact is supposed to be

purely elastic, define the trajectory of B after the impact on the wall.

x

y

A

B

0v x

O

*O

d

Figure 1

Exercise 2:

Figure 2 shows a simplified representation of a fairground attraction aimed at showing

everybody how strong you are The system is made of a horizontal track of length

dAB = connected at B with a part of a circular track of radiusR . The objective is to push a

mass m such that it goes as high as possible on the circular path. The position of any point

P on the circular path is described by the angle and the corresponding altitude is ( )h . The

acceleration of the gravity field is g .

7/26/2019 Mechanics Test 3

2/2

Part A: Friction is neglected

1 Knowing that the maximum height reached by the mass is H, express the velocity vector

at point B

2 The mass is supposed to be pushed between points A and B by a constant force F, give

the expression of Fin terms of Hgm ,, and d.

3 Find the expression of the reaction force from the track for any angular position on the

circular part in terms of ( )mhRH ,,, and g .

Part B: There is some friction between the track (linear and circular parts) and the mass

which is simulated by introducing a constant friction coefficientf.

1-

Determine the energy dissipated over segment AB 2- In what follows, the influence of the dynamic effects on the friction force is neglected

and it is assumed that, at any point along the circular path, the friction force on the

mass can be approximated as:

efmgT

cos

a- Determine the energy dissipated by friction when mass m moves fromB to a

point of altitude ( )h in terms of Rgmf ,,, and ( )h .

b-

If the maximum altitude is *H , find the force *F (supposed to be constant

along AB ) which is required.

O

x

y

re

R

P

B

A H

d

( )h

Figure 2