ACR/SEM1/GP 110/ May 2020
GP 110: Engineering Mechanics
Problem Sheet 2: Kinetics of Particles
Problem 1
60 kg woman holds a 9 kg package as she stands within an elevator which briefly accelerates
upward at a rate of g/4 as shown in Figure 1. Determine the force R which the elevator floor
exerts on her feet and the lifting force L which she exerts on the package during the acceleration
interval. If the elevator support cables suddenly and completely fail, what values would R and L
acquire?
Figure 1
Figure 2
Problem 2:
Determine the maximum speed at which the car with mass m can pass over the top point A of
the vertical curved road and still maintain contact with the road. If the car maintains this speed,
what is the normal reaction the road exerts on the car when it passes the lowest point B on the
road?
Problem 3:
The 1-kg collar P slides on the vertical bar and has a pin that slides in the curved slot as shown in
Figure 3. The vertical bar moves with constant velocity, 𝑣 = 2 𝑚/𝑠 . What are the x and y
components, with reference to the coordinate axes shown in the figure, of the total force exerted
on the collar by the vertical bar and the slotted bar when 𝑥 = 0.25 m?
Figure3
Asanga Ratnaweera, Department of Mechanical Engineering
1
ACR/SEM1/GP 110/ May 2020
Problem 4:
The small object is placed on the inner surface of the conical dish at the radius as shown in Figure
4. If the coefficient of static friction between the object and the conical surface is 0.30, for what
range of angular velocities ω about the vertical axis will the block remain on the dish without
slipping? Assume that speed changes are made slowly so that any angular acceleration may be
neglected.
Figure 5
Figure 4
Problem 5:
A small collar of mass 𝑚 is given an initial velocity of magnitude 𝑣o on the horizontal circular track
fabricated from a slender rod as shown in Figure 5. If the coefficient of kinetic friciton is 𝜇 k,
determine the distance traveled before the collar comes to rest. (Hint: Recognize that the
friction force depends on the net normal force.)
Problem 6:
The 0.8 Mg car travels over the hill having the shape of a parabola as shown in Figure 6. When
the car is at point A, it is traveling at 9 m/s and increasing its speed at 3 m/s2. Determine both
the resultant normal force and the resultant frictional force that all the wheels of the car exert
on the road the instant shown in figure. Neglect the size of the car.
Figure 6
Figure 7
Problem 7:
The robot shown in Figure 7 is programmed so that the 0.4 kg part A describes the path:
𝑟 = 1 − 0.5𝑐𝑜𝑠2𝜋𝑡 𝑚 and,
𝜃 = 1 − 0.5𝑠𝑖𝑛2𝜋𝑡 𝑟𝑎𝑑 .
Determine the polar components of force exerted on A by the robot’s jaws at 𝑡 = 2 s.
Asanga Ratnaweera, Department of Mechanical Engineering
2
ACR/SEM1/GP 110/ May 2020
Problem 8:
If the position of the 3 kg collar C on the smooth rod AB is held at r = 720 mm as shown in
Figure 8 , determine the constant angular velocity 𝜃̇, at which the mechanism is rotating about
the vertical axis.
Figure 8
Quiz # 3
The 2 kg slider fits loosely in the smooth
slot of the disk, which rotates about a
vertical axis through point O as shown in
Figure 5. The slider is free to move slightly
along the slot before one of the wires
becomes taut. If the disk starts from rest at
time t = 0 and has a constant clockwise
angular acceleration of 0.5 rad/s2, plot the
tensions in wires 1 and 2 and the
magnitude N of the force normal to the
slot as functions of time t for the interval 0
≤ t ≤ 5 s.
Figure Q3
Submission: On or before 12 midnight, Monday 11th May, 2020.
Asanga Ratnaweera, Department of Mechanical Engineering
3