Conceptual Dynamics - Independent Learning

Plane Curvilinear Motion - Contrained & Dependent Motion - Review Problems

 

RP3-1) Consider a projectile that is only acted on by gravity (i.e. no air resistance). The x-direction velocity is constant.

 

  

 

 

 

RP3-2) Consider a projectile that is only acted on by gravity (i.e. no air resistance). The y-direction velocity is constant.

 

  

 

 

 

RP3-3) Consider a projectile that is only acted on by gravity (i.e. no air resistance). The initial value of the y-direction speed is always the same as the final value of the y-direction speed.

 

  

 

 

 

RP3-4) Consider a projectile that is only acted on by gravity (i.e. no air resistance). The y-direction velocity at the peak is zero.

 

  

 

 

 

RP3-5) Consider a projectile that is only acted on by gravity (i.e. no air resistance). The x-direction acceleration is zero.

 

  

 

 

 

RP3-6) Consider a projectile that is only acted on by gravity (i.e. no air resistance). The y-direction acceleration is constant.

 

  

 

 

 

RP3-7) An astronaut performs an experiment on the surface of the moon to measure the acceleration of a falling object. The astronaut obtains an estimated acceleration of 3.1 m/s2 from her experiment. It is known that the acceleration due to gravity on the moon’s surface is approximately 1.6 m/s2. What is the most likely explanation of the difference in values?

 





 

 

 

RP3-8) Two identical balls (ball A and ball B) are dropped from the same height and are photographed at constant intervals of time as they fall. Which of the following answers most likely explains the difference in the trajectory of ball A as compared to the trajectory of ball B?

 

 





 

 

 

 

RP3-9) The five balls shown are thrown with the same initial velocity at the same angle with respect to the horizontal and from the same initial height. Each ball weighs a different amount. Neglecting air resistance, which ball will travel the farthest? Enter letters into the text fields. Do not use commas and if more than one case is enter in a single box, put them in alphabetical order.

 

 

Farthest Next Next Next Shortest

 

 

 

 

RP3-10) Consider a bi-athlete shooting a target as shown in the figure. The figure doesn’t show it, but the target is far away from the athlete, but still within the gun's range. He aims horizontally and directly at the center of the target and shoots the instant the target support snaps and the target begins to fall to the ground. Neglecting air resistance, where does the bullet hit the target?

 

 





 

 

 

 

RP3-11) Shown are six figures of archers shooting arrows from the tops of hills. The arrows are all the same and all are shot horizontally. Rank each arrow in order from longest to shortest time to reach the ground. Then rank each arrow in order from furthest horizontal distance traveled to shortest horizontal distance traveled. If you are entering more than one letter in a box, do not separate them with commas and put them in alphabetical order.

 

 

Time to reach ground:

 

Longest Next Next

 

Next Next Shortest

 

 

 

 

Horizontal distance traveled:

 

Farthest Next Next

 

Next Next Shortest

 

 

 

 

RP3-12) A car is rounding a curve at constant speed. Is the velocity also constant?

 

  

 

 

 

RP3-13) A car is rounding a curve at constant speed. Is the acceleration zero?

 

  

 

 

 

RP3-14) Consider a particle moving in 2-D space on a known path. What direction is the velocity?

 

 

 

 

RP3-15) Consider the acceleration a = (dv/dt)et + (v2/ρ)en of a particle moving in 2-D space. Explain the physical meanings of the two acceleration terms.

 

 

 

 

RP3-16) The position of a particle is given by r = bsin(ct) i + dcos(ft) j, where b = 5 m, c = 3 rad/s, d = 1 m and f = 5 rad/s. What is the magnitude of the particle's velocity and acceleration at t = 4 s?

 

v = i + j m/s

 

 

 

 

v = m/s

 

 

 

 

a = i + j m/s

 

 

 

 

a = m/s

 

 

 

 

RP3-17) A track for motorcycle racing was designed so that riders jump off a slope at 20o, from a height of 5 m. During a race it was observed that the rider and bike left the ramp at 150 km/h and remained in the air for 5 seconds. Determine the horizontal distance he traveled before striking the ground, and the maximum height he attained.

 

 

R = m

 

 

 

 

vy = t + m/s

 

 

 

 

tB = s

 

 

 

 

yB = m

 

 

 

 

h = m

 

 

 

 

RP3-18) A car drives on a circular track of radius 250 ft. The car’s speed is v = 3(t + t 2) ft/s for the time period 0 ≤ t ≤ 2 s where t is in seconds. Determine the magnitude of the car's acceleration when t = 2 s. How far has the car traveled during this period of time?

 

at = 2 = ft/s2

 

 

 

 

st = 2 = ft

 

 

 

 

RP3-19) Consider the pendulum shown. On the upswing of its motion and at the instant when θ = 20o, (dθ/dt) = 3 rad/s and (d 2θ/dt 2) = 5 rad/sec2 in the directions shown, determine the acceleration of the pendulum's head in both r-θ and x-y coordinates. The length of the pendulum bar is L = 0.5 m.

 

 

a = er + eθ m/s2

 

 

 

 

a = i + j m/s2

 

 

 

 

RP3-20) A kayak travels from the west bank to the east bank of a river with a constant velocity relative to the river current of vB/R = vB/R i. If the river current is constant and flowing in the direction shown in the figure, determine the velocity of B, the time it takes the kayak to traverse the river and the distance it ends up landing downstream (d) in terms of vB/R, vR and D.

 

 

What is the velocity of the boat?

 




 

 

 

What is the time it takes the boat to cross the river?

 




 

 

 

What is d?

 




 

 

 

RP3-21) A crate C is being pulled up an incline using motor M and the rope and pulley system shown. Determine the speed of the crate if the motor is pulling the rope in at a constant speed of 6 m/s.

 

 

vC =