The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
The School of Engineering acknowledges that the land on which we are situated is the unceded
territory of the Syilx (Okanagan) People.
APSC 181 Dynamics: Tutorial 05 – Week starting from 10th February 2024
Full Name: __________________ SIS ID: ___________ Tutorial No: 05
Class Section: 201/202
Source:
Tutorial Section: __________
Signature: ________
No. of Pages: _________
Meriam, J. L., Kraige, L. G., & Bolton, J. N. (2018). Engineering Mechanics Dynamics.
9th Edition. Hoboken, NJ. Copyright: John Wiley & Sons, Inc.
Question 1 [2/078]: A test car starts from rest on a horizontal circular track of 80‐m radius and
increases its speed at a uniform rate to reach 100 𝑘𝑚/ℎ in 10 seconds. Determine the magnitude 𝑎
of the total acceleration of the car 8 seconds after the start.
Solution:
1
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 2 [2/079]: Six acceleration vectors are shown for the car whose velocity vector is directed
forward. For each acceleration vector describe in words the instantaneous motion of the car.
Solution:
2
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 3 [2/082]: The driver of the truck has an acceleration of 0.4𝑔 as the truck passes over the
top A of the hump in the road at constant speed. The radius of curvature of the road at the top of the
hump is 98 𝑚, and the center of mass G of the driver (considered a particle) is 2 𝑚 above the road.
Calculate the speed 𝑣 of the truck.
Solution:
3
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 4 [2/084]: A sprinter practicing for the 200‐m dash accelerates uniformly from rest at A and
reaches a top speed of 40 km/h at the 60‐m mark. He then maintains this speed for the next 70 meters
before uniformly slowing to a final speed of 35 km/h at the finish line. Determine the maximum
horizontal acceleration which the sprinter experiences during the run. Where does this maximum
acceleration value occur?
Solution:
4
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 5 [2/085]: A train enters a curved horizontal section of track at a speed of 100 𝑘𝑚/ℎ and
slows down with constant deceleration to 50 𝑘𝑚/ℎ in 12 seconds. An accelerometer mounted inside
the train records a horizontal acceleration of 2 𝑚/𝑠 2 when the train is 6 seconds into the curve.
Calculate the radius of curvature 𝜌 of the track for this instant.
Solution:
5
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 6 [2/088]: The design of a camshaft‐drive system of a four-cylinder automobile engine is
shown. As the engine is revved up, the belt speed v changes uniformly from 3 𝑚/𝑠 to 6 𝑚/𝑠 over a
two‐second interval. Calculate the magnitudes of the accelerations of points 𝑃1 and 𝑃2 halfway
through this time interval.
Solution:
6
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 7 [2/090]: The car C increases its speed at the constant rate of 1.5 𝑚/𝑠 2 as it rounds the
curve shown. If the magnitude of the total acceleration of the car is 2.5 𝑚/𝑠 2 at the point A where the
radius of curvature is 200 𝑚, compute the speed 𝑣 of the car at this point.
Solution:
7
The University of British Columbia
Faculty of Applied Science, School of Engineering
Winter Term 2 (Jan – Apr, 2025)
APSC 181 Dynamics
Question 8 [2/092]: A golf ball is launched with the initial conditions shown in the figure. Determine
the radius of curvature of the trajectory and the time rate of change of the speed of the ball (a) just
after launch and (b) at apex. Neglect aerodynamic drag.
Solution:
8