Future University in Egypt
Faculty of Engineering
Engineering Physics & Math dept.
Spring 2025
Course Code: EMP130: Engineering Mechanics
Sheet (8): (Tangential and Normal) (Radial and Transverse) Components
Hint: use all dimensions in all problems as SI.
2/107) the speed of a car increases uniformly with time
from 50 km/h at A to 100 km/h at B during 10 seconds.
The radius of curvature of the hump at A is
40 m. If the magnitude of the total acceleration of
the mass center of the car is the same at B as at A,
compute the radius of curvature ρB of the dip in the
road at B. The mass center of the car is 0.6 m from
the road.
Answer: ρ = 163m
2/111) the car is traveling at a speed of 95 km/hr as it
Approaches point A. Beginning at A, the car decelerates
at a constant 2 m/sec2 until it gets to point B,
after which its constant rate of decrease of speed is 0.9 m/sec2
as it rounds the interchange ramp. Determine
the magnitude of the total car acceleration 60 m
(a) just before it gets to B, (b) just after it passes B, m
and (c) at point C.
Answer: a = 2m/s2, a = 5.6m/s2, a = 2.9m/s2
90 m
2/115) the car C increases its speed at the constant rate of 1.5 m/s2 as it rounds the curve shown. If
the magnitude of the total acceleration of the car is 2.5 m/s2 at the point A where the radius of
curvature is 200 m, compute the speed v of the car at this point.
Answer: v = 20m/s
1
Future University in Egypt
Faculty of Engineering
Engineering Physics & Math dept.
Spring 2025
Course Code: EMP130: Engineering Mechanics
Sheet (8): (Tangential and Normal) (Radial and Transverse) Components
2/122) the particle P starts from rest at point A at time t = 0
and changes its speed thereafter at a constant
rate of 2g as it follows the horizontal path
shown. Determine the magnitude and direction
of its total acceleration (a) just before point B,
(b) just after point B, and (c) as it passes point C.
State your directions relative to the x-axis shown
(CCW positive).
Answer: a = 19.6m/s2, Ɵ = 0, a = 38.9m/s2, Ɵ = 59, a = 97m/s2,
Ɵ = 78
2/133)
A car P travels along a straight road with a constant
Speed v = 100 km/hr . At the instant when the
30 m
Angle Ө = 60o , determine the values of ṙ in m/sec
And in deg/sec.
Answer: ṙ = 13.8m/s, = -39 deg/s
2/137) The drag racer P starts from rest at the start line S
and then accelerates along the track. When it has
traveled 100 m, its speed is 45 m/s. For that instant,
determine the values of ṙ and relative to
axes fixed to an observer O in the grandstand G as
shown.
Answer: ṙ = 42m/s, = -0.14 r/s
2/142) The piston of the hydraulic cylinder gives pin A a
constant velocity = 1.5 m/s in the direction
shown for an interval of its motion. For the instant
when Ө = 60o, determine ṙ,ȑ , ,Ӫ where r =
150 mm
Answer: ṙ = -0.75m/s ,ȑ = 9.7m/s2 , = 7.5r/s, Ӫ = 65r/s2
2
Future University in Egypt
Faculty of Engineering
Engineering Physics & Math dept.
Spring 2025
Course Code: EMP130: Engineering Mechanics
Sheet (8): (Tangential and Normal) (Radial and Transverse) Components
2/149) The cam is designed so that the center of the roller
A which follows the contour moves on a limaçon defined
By r = b – c cosӨ , where b > c. If the cam
does not rotate, determine the magnitude of the
total acceleration of A in terms of Ө. if the slotted
arm revolves with a constant counterclockwise
angular rate = ω.
Answer:
A={ }2 + { }2
