Dynamics Test 1

Dynamics:

1. Kinematics - concerned with the geometric aspects of motion 2. Kinetics - concerned with the forces causing the motion

1. A particle has an initial velocity of 3 ft/s to the left at s0 = 0 ft. Determine its position when t = 3 s if the acceleration is 2 ft/s2 to the right. Note: use formula s=ut+1/2(a)(t^2) > -3*3+.5(2)(3^2)=0 A) 0.0 ft B) 6.0 ft <-- C) 18.0 ft --> D) 9.0 ft -->

A) 0.0 ft

Determine the speed of block B. Note 2 pullies at 2 m/s > 2/2 =1m/s A) 1 m/s B) 2 m/s C) 4 m/s D) None of the above.

A) 1 m/s

Determine the acceleration of the block. Note: 2(60Sin30) - 5*9.81 =5*a (assume up is +) A) 2.20 m/s^2 up B) 3.17 m/s^2 C) 11.0 m/s^2 up D) 4.26 m/s^2 up

A) 2.20 m/s^2 up

If a particle has moved from A to B along the circular path in 4s, what is the average velocity of the particle? Note: use [(XsubB-XsubA)i + (YsubB-YsubA)]/t t=4 and radius=5 diameter=10 so SsubB=10 ...> 10/4=2.5i m/s A) 2.5 i m/s B) 2.5 i +1.25 j m/s C) 1.25 p i m/s D) 1.25 p j m/s

A) 2.5 i m/s

A projectile is given an initial velocity vsubo at an angle f above the horizontal. The velocity of the projectile when it hits the slope is ____________ the initial velocity vsubo. A) less than B) equal to C) greater than D) None of the above.

A) less than

If the motion of one particle is dependent on that of another particle, each coordinate axis system for the particles _______ A) should be directed along the path of motion. B) can be directed anywhere. C) should have the same origin. D) None of the above.

A) should be directed along the path of motion.

In curvilinear motion, the direction of the instantaneous acceleration is always A)tangent to the hodograph. B)perpendicular to the hodograph. C)tangent to the path. D)perpendicular to the path.

A) tangent to the hodograph

The radial component of velocity of a particle moving in a circular path is always A) zero. B) constant. C) greater than its transverse component. D) less than its transverse component.

A) zero.

The time of flight of a projectile, fired over level ground, with initial velocity Vo at angle θ, is equal to? A) (vo sin q)/g B) (2vo sin q)/g C) (vo cos q)/g D) (2vo cos q)/g

B) (2vsubo sin q)/g

Determine the velocity vector of block A when block B is moving downward with a speed of 10 m/s. Note use triangle 4/3 A) (8i + 6j) m/s B) (4i + 3j) m/s C) (-8i - 6j) m/s D) (3i + 4j) m/s

B) (4i + 3j) m/s

The position of a particle is given as r = (4t^2 i - 2x j) m. Determine the particle's acceleration. Note multiply i comp times j to get rid of x > 2*4t^2 and take second derivative to get acceleration. A) (4 i +8 j ) m/s^2 B) (8 i -16 j ) m/s^2 C) (8 i ) m/s^2 D) (8 j ) m/s^2

B) (8 i -16 j ) m/s^2

A particle is moving with an initial velocity of v = 12 ft/s and constant acceleration of 3.78 ft/s2 in the same direction as the velocity. Determine the distance the particle has traveled when the velocity reaches 30 ft/s. Note: v=u+at solve for a A) 50 ft B) 100 ft C) 150 ft D) 200 ft

B) 100 ft

If a particle starts from rest and accelerates according to the graph shown, the particle's velocity at t = 20 s is? Note: (Area under the curve)=(10*20)/2; Also deltav=v2-v1=v2-0=100 A) 200 m/s B) 100 m/s C) 0 D) 20 m/s

B) 100 m/s

1.For the path defined by r = theta^2 , the angle y at theta = 0.5 rad is? Note: TanY = rdtheta/dr = theta^2/(d/dtheta)*theta^2= theta^2/2theta... solve for 0.5 and take inverse tangent. A) 10º B) 14º C) 26º D) 75º

B) 14º

If a car has the velocity curve shown, determine the time t necessary for the car to travel 100 meters. Note: S=S0=V0*t+1/2a*t^2, S=100, V0=0, a=75/6) know! a=dv/dt A) 8 s B) 4 s C) 10 s D) 6 s

B) 4 s

If a particle moving in a circular path of radius 5 m has a velocity function v = 4t^2 m/s, what is the magnitude of its total acceleration at t = 1 s? Note: aubt=deriv of v and asubn= v^2/rho, compute magnitude... A) 8 m/s2 B) 8.6 m/s2 C) 3.2 m/s2 D) 11.2 m/s2

B) 8.6 m/s^2

In dynamics, the friction force acting on a moving object is always ________ A) in the direction of its motion. B) a kinetic friction. C) a static friction. D) zero.

B) a kinetic friction.

The slope of a v-t graph at any instant represents instantaneous A) velocity. B) acceleration. C) position. D) jerk.

B) acceleration.

When particles are interconnected by a cable, the motions of the particles are ______ A) always independent. B) always dependent. C) not always dependent. D) None of the above.

B) always dependent.

The "normal" component of the equation of motion is written as SumFn=man, where SumFn is referred to as the _______. A) impulse B) centripetal force C) tangential force D) inertia force

B) centripetal force

The directions of the tangential acceleration and velocity are always A) perpendicular to each other. B) collinear. C) in the same direction. D) in opposite directions.

B) collinear.

The horizontal component of velocity remains _________ during a free-flight motion. A) zero B) constant C) at 9.81 m/s2 D) at 32.2 ft/s2

B) constant

The magnitude of the normal acceleration is A) proportional to radius of curvature. B) inversely proportional to radius of curvature. C) sometimes negative. D) zero when velocity is constant.

B) inversely proportional to radius of curvature.

If r is zero for a particle, the particle is A) not moving. B) moving in a circular path. C) moving on a straight line. D) moving with constant velocity.

B) moving in a circular path

In dynamics, a particle is assumed to have _________. A) both translation and rotational motions B) only a mass C) a mass but the size and shape cannot be neglected D) no mass or size or shape, it is just a point

B) only a mass

The tangential acceleration of an object A) represents the rate of change of the velocity vector's direction. B) represents the rate of change in the magnitude of the velocity. C) is a function of the radius of curvature. D) Both B and C.

B) represents the rate of change in the magnitude of the velocity.

2.When the forces acting on a particle are resolved into cylindrical components, friction forces always act in the __________ direction. A) radial B) tangential C) transverse D) None of the above.

B) tangential

The normal component of acceleration represents A) the time rate of change in the magnitude of the velocity. B) the time rate of change in the direction of the velocity. C) magnitude of the velocity. D) direction of the total acceleration.

B) the time rate of change in the direction of the velocity.

Two blocks are interconnected by a cable. Which of the following is correct? Note: velocity are inversely proportional wince there's 1 pully. v of A = -v of B A) (vx)A= - (vx)B B) vA= - vB C) (vy)A= - (vy)B D) All of the above.

B) vA= - vB

A 10 lb particle has forces of F1= (3i + 5j) lb and F2= (-7i + 9j) lb acting on it. Determine the acceleration of the particle. Note: Resultant force, F = F1 + F2 = 3i + 5j -7i + 9j = (-4i + 14j) lb now multiply with g to convert this force lbf - F = (-4i + 14j) * 32.2 lbf = (-128.8i + 450.8j) lbf So, acceleration of the particle, a = F / m = F / 10 = (-12.88i + 45.08j) ft/s^2 (12.9i + 45j) ft/s^2 A) (-0.4 i + 1.4 j) ft/s^2 B) (-4 i + 14 j) ft/s^2 C) (-12.9 i + 45 j) ft/s^2 D) (13 i + 4 j) ft/s^2

C) (-12.9 i + 45 j) ft/s^2

A 20 lb block is moving along a smooth surface. If the normal force on the surface at A is 10 lb, the velocity is ________. Note: W-N=mv^2/rho > W-N=W/G*v^2/rho A) 7.6 ft/s B) 9.6 ft/s C) 10.6 ft/s D) 12.6 ft/s

C) 10.6 ft/s

Determine the speed of block B when block A is moving down at 6 ft/s while block C is moving down at 18 ft/s. Note: Va=6, Vb=2Vb, Vc=-18..... 6+2Vb+18=0 > 2Vb=-24 Vb=-12ft/s A) 24 ft/s B) 3 ft/s C) 12 ft/s D) 9 ft/s

C) 12 ft/s

The block has a mass of 20 kg and a speed of v = 30 m/s at the instant it is at its lowest point. Determine the tension in the cord at this instant. Note: Use T-mg=mar > T=mar+mg > T=mv^2/rho+mg A) 1596 N B) 1796 N C) 1996 N D) 2196 N

C) 1996 N

In a projectile motion problem, what is the maximum number of unknowns that can be solved? A) 1 B) 2 C) 3 D) 4

C) 3

If the position of a particle is defined by r = [(1.5t2 + 1) i + (4t - 1) j ] (m), its speed at t = 1 s is ________. Note: Take derivatives of both i and j then sub in for t=1 then solve for magnitude sqrt 3^2 +4^2 = 5m/s A) 2 m/s B) 3 m/s C) 5 m/s D) 7 m/s

C) 5 m/s

A particle traveling in a circular path of radius 300 m has an instantaneous velocity of 30 m/s and its velocity is increasing at a constant rate of 4 m/s^2. What is the magnitude of its total acceleration at this instant? Note: 4 m/s^2 = asubt tangential, asubn = v^2/rho or radius, compute magnitude... A) 3 m/s2 B) 4 m/s2 C) 5 m/s2 D) -5 m/s2

C) 5 m/s2

Determine the tension in the cable when the 400 kg box is moving upward with a 4 m/s^2 acceleration. Note: tension in the cable= m(g+a) = 400*(9.81+4)= 5524 N A) 2265 N B) 3365 N C) 5524 N D) 6543 N

C) 5524 N

1.The downward acceleration of an object in free-flight motion is A) zero. B) increasing with time. C) 9.81 m/s2. D) 9.81 ft/s2.

C) 9.81 m/s2.

2.If needing to solve a problem involving the pilot's weight at Point C, select the approach that would be best. A) Equations of Motion: Cylindrical Coordinates B) Equations of Motion: Normal & Tangential Coordinates C) Equations of Motion: Polar Coordinates D) No real difference - all are bad. E) Toss up between B and C.

C) Equations of Motion: Polar Coordinates

In a polar coordinate system, the velocity vector can be written as v = vrur + vθuθ = r'ur + rtheta'uq. The term theta is called A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration.

C) angular velocity.

In a polar coordinate system, the velocity vector can be written as v = vrur + vθuθ = rur + rquq. The term q is called A) transverse velocity. B) radial velocity. C) angular velocity. D) angular acceleration.

C) angular velocity.

If a particle is connected to a spring, the elastic spring force is expressed by F = ks . The "s" in this equation is the A) spring constant. B) un-deformed length of the spring. C) difference between deformed length and un-deformed length. D) deformed length of the spring.

C) difference between deformed length and un-deformed length.

The average speed is defined as __________. A) Delta r/Delta t B) Delta s/Delta t C) s sub T/Delta t D) None of the above.

C) s sub T/Delta t

1.The normal force which the path exerts on a particle is always perpendicular to the _________ A) radial line. B) transverse direction. C) tangent to the path. D) None of the above.

C) tangent to the path.

. Displacement of a particle over a given time interval equals the area under the ___ graph during that time. A) a-t B) a-s C) v-t D) s-t

C) v-t

If a particle moves along a curve with a constant speed, then its tangential component of acceleration is A) positive. B) negative. C) zero. D) constant.

C) zero.

If a particle moves in a circular path with constant velocity, its radial acceleration is A) zero. B) r'' C) − rtheta^ 2. D) 2rtheta .

C) − rtheta^ 2.

In curvilinear motion, the direction of the instantaneous velocity is always A)tangent to the hodograph. B)perpendicular to the hodograph. C)tangent to the path. D)perpendicular to the path.

C)tangent to the path.

A particle has an initial velocity of 30 ft/s to the left. If it then passes through the same location 5 seconds later with a velocity of 50 ft/s to the right, the average velocity of the particle during the 5 s time interval is _______. Note: vsubavg = displacement/time > 0/5s = 0 ft/s A) 10 ft/s --> B) 40 ft/s --> C) 16 m/s --> D) 0 ft/s

D) 0 ft/s

A particle moves along a horizontal path with its velocity varying with time as shown. The average acceleration of the particle is _________. Note: formula a=v-u/tsub2-tsub1 measured in m/s^2 A) 0.4 m/s2 --> B) 0.4 m/s2 <-- C) 1.6 m/s2 --> D) 1.6 m/s2 <--

D) 1.6 m/s2 left

If r = theta^2 and theta = 2t, find the magnitude of r ̇ and θ ̈ when t = 2 seconds. Note: r = theta^2 -> theta= 2t -> r = (2t)^2 = 4t^2 r' = 8t -> r' at t= 2s = 8*2 = 16 theta = 2t => theta' = 2 => theta" = 0 A) 4 cm/sec, 2 rad/sec2 B) 4 cm/sec, 0 rad/sec2 C) 8 cm/sec, 16 rad/sec2 D) 16 cm/sec, 0 rad/sec2

D) 16 cm/sec, 0 rad/sec2

The path of a particle is defined by y = 0.5x^2. If the component of its velocity along the x-axis at x = 2 m is vx = 1 m/s, its velocity component along the y-axis at this position is ____. Note:n Take derivative and solve for x=2 A) 0.25 m/s B) 0.5 m/s C) 1 m/s D) 2 m/s

D) 2 m/s

The particle in Problem 1 stops moving at t = _______. Note: a=10-kt=(10-.5t) use dv=adt where limit of integration v1=0 v2=0 t1=0 t2=t A) 10 s B) 20 s C) 30 s D) 40 s

D) 40 s

If the cable has a tension of 3 N, determine the acceleration of block B. Note: 2T-wB=wA...... wB= 4*9.81, wA=-4aB A) 4.26 m/s^2 up B) 4.26 m/s^2 down C) 8.31 m/s^2 up D) 8.31 m/s^2 down

D) 8.31 m/s^2 down

The positive n direction of the normal and tangential coordinates is ____________. A) normal to the tangential component B) always directed toward the center of curvature C) normal to the bi-normal component D) All of the above.

D) All of the above.

The radial component of acceleration of a particle moving in a circular path is always A) negative. B) directed toward the center of the path. C) perpendicular to the transverse component of acceleration. D) All of the above.

D) All of the above.

1.When a pilot flies an airplane in a vertical loop of constant radius r at constant speed v, his apparent weight is maximum at A) Point A B) Point B (top of the loop) C) Point C D) Point D (bottom of the loop)

D) Point D (bottom of the loop)

A particle has an initial velocity vo at angle f with respect to the horizontal. The maximum height it can reach is when A) f = 30° B) f = 45° C) f = 60° D) f = 90°

D) f = 90°

Select the correct a-t graph for the velocity curve shown.

D) is correct

The speed of a particle in a cylindrical coordinate system is • A) r B) rq C) sqrt(rq)2 + (r)2 D) sqrt(rq)2 + (r)2 + (z)2

D) sqrt(rq)2 + (r)2 + (z)2

The speed of a particle in a cylindrical coordinate system is Note cylindrical will include z A) r' B) rtheta' C) sqrt(rtheta')^2 + (r')^2 D) sqrt(rtheta)^2 + (r')^2 + (z')^2

D) sqrt(rtheta)^2 + (r')^2 + (z')^2

A 10 kg sack slides down a smooth surface. If the normal force at the flat spot on the surface, A, is 98.1 N () , the radius of curvature is ____. Note: N-mg=mv^2/rho.... solve for rho A) 0.2 m B) 0.4 m C) 1.0 m D)None of the above

D)None of the above

Mechanics:

The study of how bodies react to the forces acting on them.