Dynamics Revision

Chapter 13

[1] The crane lifts the 700-kg bin with an initial acceleration of 3m/s2. Determine the

force in each of the supporting cables due to this motion.

[2] The baggage truck A has a mass of 800kg and is used to pull the two cars, each

with mass 300kg. If the tractive force F on the truck is F = 480N, determine the

initial acceleration of the truck. What is the acceleration of the truck if the

coupling at C suddenly fails? The car wheels are free to roll. Neglect the mass of

the wheels.

[3] The driver attempts to tow the crate using a rope that has a tensile strength of

1kN. If the crate is originally at rest and has a weight of 2.5kN (≈ 250kg),

determine the greatest acceleration it can have if the coefficient of static friction

between the crate and the road is µs = 0.4, and the coefficient of kinetic friction is

µk = 0.3.

[4] The 200-kg snowmobile with passenger is travelling down the hill such that when

it is at point A, it is travelling at 4m/s and increasing its speed at 2m/s2. Determine

the resultant normal force and the resultant frictional force exerted on the tracks at

this instant. Neglect the size of the snowmobile.

[5] The roller coaster car and passenger have a total weight of 3000N (≈300 kg) and

starting from rest at A travel down the track that has the shape shown. Determine

the normal force of the tracks on the car when the car is at point B, where it has a

velocity of 4.5m/s. Neglect friction and the size of the car and passenger.

[6] The 10N (≈1 kg) collar slides along the smooth horizontal spiral rod, r = (2θ) m,

where θ is in radians. If its angular rate of rotation is constant and equals θ.

=

4rad/s, determine the tangential force P needed to cause the motion and the

normal force that the roda exerts on the spool at the instant θ=90°.

Chapter 14

[7] The collar has a mass of 20kg and rests on the smooth rod. Two springs are

attached to it and the ends of the rod as shown. Each spring has an uncompressed

length of 1m. If the collar is displaced s = 0.5m and released from rest, determine

its velocity at the instant it returns to the point s =0.

[8] The cyclist travels to point A, pedalling until he reaches a speed Va = 4m/s. he

then coasts freely up the curved surface. Determine how high he reaches up the

surface before he comes to a stop. Also, what are the resultant normal force on the

surface at this point and his acceleration? The total mass of the bike and man is

75kg. Neglect friction, the mass of the wheels, and the size of the bicycle.

[9] The ball has a weight of 75N (≈7.5kg) and is fixed to a rod having a negligible

mass. If it is released from rest when θ = 0°, determine the angle θ at which the

compressive force in the rod becomes zero.

[10] The roller coaster car has a speed of 5m/s when it is at the crest of a

vertical parabolic track. Determine the car’s velocity and the normal force it

exerts on the track when it reaches point B. Neglect friction and the mass of the

wheels. The total weight of the car and the passengers is 2000N (≈200kg).

Chapter 15

[11] The uniform beam has a weight of 25 kN (≈2500kg). Determine the

average tension in each of the two cables AB and AC if the beam is given an

upward speed of 4m/s in 1.5s starting from rest. Neglect the mass of the cables.

[12] The 250 N (≈ 25kg) cabinet is subjected to the force F = 10/(t+1) N where

t is in seconds. If the cabinet is initially moving down the plane with a velocity of

3m/s, determine how long it will take before the cabinet comes to a stop. F

always acts parallel to the plane. Neglect the size of the rollers.

[13] When the 2-N (≈ 0.2kg) ball is fired, it leaves the ground at an angle of

40° from the horizontal and strikes the ground at the same elevation a distance of

40m away. Determine the impulse given to the ball.

[14] A 50 kg boy walks forward over the surface of the 30-kg cart with a

constant speed of 1m/s relative to the cart. Determine the cart’s speed and its

displacement at the moment he is about to step off. Determine the cart’s speed

and its displacement at the moment he is about to step off. Neglect the mass of the

wheels and assume the cart and boy are originally at rest.

[15] The barge B weighs 150kN (≈ 15 000kg) and supports an automobile

weighing 15kN (≈1500 kg). If the barge is not tied to the pier P and someone

drives the automobile to the other side of the barge for unloading, determine how

far the barge moves away from the pier. Neglect the resistance of the water.

[16] A small particle having a mass m is placed inside the semicircular tube.

The particle is placed at the position shown and released. Apply the principle of

angular momentum about point O (ΣMo=Ho.

), and show that the motion of the

particle is governed by the differential equation θθ sin)/(..

Rg+ =0.

[17] Determine the velocity of the slider block at C at the instant θ=45°, if link

AB is rotating at 4rad/s.

[18] If at a given instant, point B has downward velocity of VB = 3m/s,

determine the velocity of point A at this instant. Notice that for this motion to

occur, the wheel must slip at A.

[19] If disk D has a constant angular velocity ωD = 2rad/s, determine the

angular velocity of disk A at the instant θ = 60°.

[20] The pinion gear A rolls on the fixed gear rack B with an angular velocity

ω = 4 rad/s. Determine the velocity of the gear rack C.

[21] The slider block C is moving 2m/s up the incline. Determine the angular

velocities of links AB and BC and the velocity of point B at the instant shown.

[22] If the collar at C is moving downward to the left at Vc = 8m/s, determine

the angular velocity of link AB at the instant shown.

[23] The flywheel rotates with an angular velocity ω = 2 rad/s and angular

acceleration α = 6rad/s2. Determine the angular acceleration of links AB and BC

at this instant.

[24] The disk rotates with the angular motion shown. Determine the angular

velocity and angular acceleration of the slotted link AC at this instant. The peg at

B is fixed to the disk.

Chapter 17

[25] The 20N (≈2kg) bottle rests on the check-out conveyor at a grocery store.

If the coefficient of static friction is µs =0.2, determine the largest acceleration the

conveyor can have without causing the bottle to slip or tip. The centre of gravity

is at G.

[26] The assembly has a mass of 8Mg and is hoisted using the boom and pulley

system. If the winch at B draws in the cable with an acceleration of 2m/s2 ,

determine the compressive force in the hydraulic cylinder needed to support the

boom. The boom has a mass of 2Mg and mass centre at G.

[27] The crate of mass m is supported on a cart of negligible mass. Determine

the maximum force P that can be applied a distance d from the cart bottom

without causing the crate to tip on the cart.

[28] The crate C has a weight of 1500N (≈150 kg) and rests on the truck

elevator for which the coefficient of static friction is µs = 0.4. Determine the

largest initial angular acceleration α, starting from rest, which the parallel links

AB and DE can have without causing the crate to slip. No tipping occurs.

The two 3kg rods EF and HI are fixed (welded) to the link AC at E. Determine the

normal force NE. shear force VE, and moment ME, which the bar AC exerts on FE at E if

at the instant θ =30° link AB has an angular velocity ω = 5rad/s and an angular

acceleration α = 8 rad/s2 as shown.