Tutorial for Applied Mechanics II, 2019
Tutorial 1: Energy and Momentum Methods of Particle
1 A small block starts from rest at point A and slides down the inclined plane as shown. What distance along the
horizontal plane will it travel before coming to rest? The coefficient of kinetic of friction between the block
and either plane is 0.3. Assume that the initial velocity with which it starts to move along BC is of the same
magnitude as that gained in sliding from A to B. [6 m]
Figure 1 Figure 2
2 A 100 lb body moves along the two inclines for which the coefficient of friction is 0.3. If the body starts from
rest at A and slides 200 ft. down the 30° incline, how far will it then move along the other incline? What will
be its velocity when it returns to B? [57.2 ft, 36.4 ft/s]
3 The 10 kg block A and the 4-kg block B are both at a height h = 0.5 m above the ground when the system is
released from rest. After A hits the ground without rebound it is observed that B reaches a maximum height of
1.18 m. Determine (a) the speed of A just before impact, (b) the amount of energy dissipated by the axle
friction in the pulley. [1.879 m/s, 4.71 J]
B
A
h
Figure 3 Figure 4
4 The two blocks shown are released from rest. Neglecting the masses of the pulleys and effect of friction in the
pulleys and knowing that the coefficient of friction between blocks and the incline are µs=0.25 and µk=0.20,
determine (a) the velocity of block A after it has moved 0.5 m, (b) the tension in the cable. [1.152 m/s ⦫30°,
18.792 N]
5 Two blocks A and B of mass 8 kg and 10 kg respectively are connected by a cord which passes over pulleys a
shown. A 6 kg collar C is placed on block A and the system is released from rest. After the blocks move 108
m, collar C is removed and blocks A and B continue to move. Determine the speed of block A just before it
strikes the ground. [1.683 m/s, ]
2
, Tutorial for Applied Mechanics II, 2019
Figure 6
Figure 5
6 A 4 kg collar C slides on a horizontal rod between springs A and B. If the collar is pushed to the right until
spring B is compressed 50 mm and released, determine the distance through which the collar will travel,
assuming (a) no friction between the collar and the rod, (b) a coefficient of friction µ k=0.35. [341 mm, 182.0
mm]
7 The smooth plug has a weight of 89 N and is pushed against a series of Belleville spring washer so that the
compression in the spring is x = 15.2 cm. If the force of the spring on the plug is F = (3x1/3) N, where x in
given in m, determine the speed of the plug after it moves away from the spring. Neglect friction. [0.2 m/s]
Figure 7 Figure 8
8 The crate, which has a mass of 100 kg, is subjected to the action of the two forces. If it is originally at rest,
determine the distance it slides in order to attain a speed of 6 m/s. The coefficient of kinetic friction between
the crate and the surface is µk = 0.2. [3.54 m]
9 A weight of W N is suspended from a vertical spring whose modulus is K N/m. The weight is pulled down S
m from its equilibrium position and then released. Determine its velocity when it returns to its equilibrium
position.
10 A weight W is attached to one end of a stiff rod of length L and negligible weight that is hinged to a horizontal
position and allowed to swing freely in a vertical arc. Through what angle must it swing to cause a tension in
of 1.5 W? [30°]
11 In the figure shown, by how much should the spring be compressed so that it will cause the 450 g pellet to
travel completely around the friction less vertical loop? What force is exerted by the track upon the pellet
when it is at position B? The value of spring constant k = 600 N/m. [0.192 m, 13.28 N]
3
, Tutorial for Applied Mechanics II, 2019
C
1m
B
K = 500 N /m
4m
K = 600 N /m
A
3m
Figure 11
Figure 12
12 Neglect friction of the 500 g collar against its vertical guide and compute the velocity of the collar after it has
fallen 7 m starting from rest in the position shown in figure. The unstretched length of spring is 2 m. [64.1 m/s]
13 A spring is used to stop a 75 kg package which is moving down a 20° incline. The spring has a constant K =
25 kN/m, and is held by cables so that it is initially compressed 100 mm. If the velocity of the package is 6 m/s
when it is 10 m from the spring in bringing the package to rest assume μ =0.2, determine the maximum
deformation in the spring. [360 mm]
6
m
/s
75
10
kg
m
Cable
20°
Figure 13
Figure 14
14 A 273 kg block slides down an incline having slope of 4 vertical to 3 horizontal. It starts from rest and after
moving 1.8 m. striker a spring whose modulus is 18 N/cm. If the coefficient of friction is 0.2, determine the
maximum deformation of the spring and the maximum velocity of the block. [3.172 m, 5.546 m/s]
15 The 0.5 kg ball of negligible size is fired up the vertical circular track using the spring plunger. The plunger
keeps the spring compressed 0.08 m when s = 0. Determine how far s it must be pulled back and released so
that the ball will begin to leave the track when θ = 135° [s = 179 mm]
Figure 16
Figure 15
16 A 2 kg collar can slide without friction along a horizontal rod and is in equilibrium at A when it is pushed
25mm to the right and is released from rest. The springs are undeformed when the collar is at A and the
constant of each spring is 500kN/m. Determine the maximum velocity of the collar. [14.12m/s]
4
Tutorial 1: Energy and Momentum Methods of Particle
1 A small block starts from rest at point A and slides down the inclined plane as shown. What distance along the
horizontal plane will it travel before coming to rest? The coefficient of kinetic of friction between the block
and either plane is 0.3. Assume that the initial velocity with which it starts to move along BC is of the same
magnitude as that gained in sliding from A to B. [6 m]
Figure 1 Figure 2
2 A 100 lb body moves along the two inclines for which the coefficient of friction is 0.3. If the body starts from
rest at A and slides 200 ft. down the 30° incline, how far will it then move along the other incline? What will
be its velocity when it returns to B? [57.2 ft, 36.4 ft/s]
3 The 10 kg block A and the 4-kg block B are both at a height h = 0.5 m above the ground when the system is
released from rest. After A hits the ground without rebound it is observed that B reaches a maximum height of
1.18 m. Determine (a) the speed of A just before impact, (b) the amount of energy dissipated by the axle
friction in the pulley. [1.879 m/s, 4.71 J]
B
A
h
Figure 3 Figure 4
4 The two blocks shown are released from rest. Neglecting the masses of the pulleys and effect of friction in the
pulleys and knowing that the coefficient of friction between blocks and the incline are µs=0.25 and µk=0.20,
determine (a) the velocity of block A after it has moved 0.5 m, (b) the tension in the cable. [1.152 m/s ⦫30°,
18.792 N]
5 Two blocks A and B of mass 8 kg and 10 kg respectively are connected by a cord which passes over pulleys a
shown. A 6 kg collar C is placed on block A and the system is released from rest. After the blocks move 108
m, collar C is removed and blocks A and B continue to move. Determine the speed of block A just before it
strikes the ground. [1.683 m/s, ]
2
, Tutorial for Applied Mechanics II, 2019
Figure 6
Figure 5
6 A 4 kg collar C slides on a horizontal rod between springs A and B. If the collar is pushed to the right until
spring B is compressed 50 mm and released, determine the distance through which the collar will travel,
assuming (a) no friction between the collar and the rod, (b) a coefficient of friction µ k=0.35. [341 mm, 182.0
mm]
7 The smooth plug has a weight of 89 N and is pushed against a series of Belleville spring washer so that the
compression in the spring is x = 15.2 cm. If the force of the spring on the plug is F = (3x1/3) N, where x in
given in m, determine the speed of the plug after it moves away from the spring. Neglect friction. [0.2 m/s]
Figure 7 Figure 8
8 The crate, which has a mass of 100 kg, is subjected to the action of the two forces. If it is originally at rest,
determine the distance it slides in order to attain a speed of 6 m/s. The coefficient of kinetic friction between
the crate and the surface is µk = 0.2. [3.54 m]
9 A weight of W N is suspended from a vertical spring whose modulus is K N/m. The weight is pulled down S
m from its equilibrium position and then released. Determine its velocity when it returns to its equilibrium
position.
10 A weight W is attached to one end of a stiff rod of length L and negligible weight that is hinged to a horizontal
position and allowed to swing freely in a vertical arc. Through what angle must it swing to cause a tension in
of 1.5 W? [30°]
11 In the figure shown, by how much should the spring be compressed so that it will cause the 450 g pellet to
travel completely around the friction less vertical loop? What force is exerted by the track upon the pellet
when it is at position B? The value of spring constant k = 600 N/m. [0.192 m, 13.28 N]
3
, Tutorial for Applied Mechanics II, 2019
C
1m
B
K = 500 N /m
4m
K = 600 N /m
A
3m
Figure 11
Figure 12
12 Neglect friction of the 500 g collar against its vertical guide and compute the velocity of the collar after it has
fallen 7 m starting from rest in the position shown in figure. The unstretched length of spring is 2 m. [64.1 m/s]
13 A spring is used to stop a 75 kg package which is moving down a 20° incline. The spring has a constant K =
25 kN/m, and is held by cables so that it is initially compressed 100 mm. If the velocity of the package is 6 m/s
when it is 10 m from the spring in bringing the package to rest assume μ =0.2, determine the maximum
deformation in the spring. [360 mm]
6
m
/s
75
10
kg
m
Cable
20°
Figure 13
Figure 14
14 A 273 kg block slides down an incline having slope of 4 vertical to 3 horizontal. It starts from rest and after
moving 1.8 m. striker a spring whose modulus is 18 N/cm. If the coefficient of friction is 0.2, determine the
maximum deformation of the spring and the maximum velocity of the block. [3.172 m, 5.546 m/s]
15 The 0.5 kg ball of negligible size is fired up the vertical circular track using the spring plunger. The plunger
keeps the spring compressed 0.08 m when s = 0. Determine how far s it must be pulled back and released so
that the ball will begin to leave the track when θ = 135° [s = 179 mm]
Figure 16
Figure 15
16 A 2 kg collar can slide without friction along a horizontal rod and is in equilibrium at A when it is pushed
25mm to the right and is released from rest. The springs are undeformed when the collar is at A and the
constant of each spring is 500kN/m. Determine the maximum velocity of the collar. [14.12m/s]
4
