Describing Motion Verbally with Speed and Velocity
UCM.C – Force – Original Assignment Name:
The Centripetal Force Requirement
Concepts
Review Questions:
1. The net force acting upon an object is ______as the direction of the object's acceleration.
a. in the same direction b. in the opposite direction
c. ... nonsense! There is no simple rule which relates the direction of the a and Fnet vectors.
2. Consider the top view of the clockwise motion of an object shown at the right. Draw an arrow to indicate the direction of the ...a. acceleration vector at location A.
b. velocity vector at location C.
c. velocity vector at location D.
Label your arrows with an a (for acceleration) and a v (for velocity). /
Force Analysis of Circular Motion:
Every instance of the motion of an object in a circle or along a circular turn involves some force that is directed inward or centripetally. The centripetal force is an adjective to describe the net force; it is not actually a new force to be added to an already lengthy list - including friction, gravity, applied, tension, normal, spring, air resistance, etc. Rather, the centripetal force requirement is a principle that states that in order to have the motion of an object in a circle, there must be an inward net force to sustain the inward acceleration.
3. In each of the following instances, identify the type of the force that fulfills the centripetal force requirement. That is, identify the inward force acting upon the bold-faced object.
Types of Forces Answer Bank - Normal Friction Gravitational Tension or a combo…
Description of a Circular-Type Motion / Centripetal Forcea. A planet is orbiting the sun.
b. A bucket (filled with water) is held by a string and whirled in a horizontal circle.
c. Passengers on the CliffHanger amusement park ride (a barrel ride) are rotated rapidly in a circle.
d. The moon is orbiting the Earth.
e. A car is making a turn along a level roadway.
f. A car is making a turn along a banked exit ramp.
g. In football, a halfback leans in and rounds the corner to head up field.
h. A roller coaster car is at the top of a circular loop (on the inside of the track).
i. A roller coaster car is at the bottom of a circular loop (on the inside of the track).
j. Clothes move in a circle during the spin cycle in a washing machine.
4. Consider the diagram in question #2 on the front side. Draw an arrow on the diagram to indicate the direction of the net force vector at both locations B and E. Label the vector with an F (for force).
5. Consider a roller coaster car passing through a clothoid loop. Two strategic positions on the loop are the top and the bottom of the loop. In the diagrams below, draw force vectors on the riders to depict the direction and the magnitude of the two forces acting upon the riders. The size of the force should be approximately equal to the size of the vector arrow. Label the two arrows according to type - Fgrav and Fnorm.
6. When the roller coaster car is at the bottom of the loop, the direction of the acceleration and the net force is directed ______(up, down). When the roller coaster car is at the top of the loop, the direction of the acceleration and the net force is directed ______(up, down).
7. In order for the conditions described in question #6 above to be true, how does the magnitude of the normal force compare to the magnitude of the gravity force at the two locations. Put a greater than (>) or a less than (<) symbol in the blanks below.
Loop Bottom: Fnorm _____ Fgrav Loop Top: Fnorm _____ Fgrav
8. A person's sensation of weight is due to the presence of a normal force upon their body. Usually, this normal force is of the same magnitude as the force of gravity. So a 600 Newton person typically feels 600 N of normal force to provide a sensation of how much they weigh. When the normal force becomes greater than or less than the force of gravity, a person has a sensation of feeling heavy or feeling light. Where on the roller coaster loop would a person most likely feel heavy - top or bottom? ______Explain your answer.
9. TRUE or FALSE:
The centripetal force is a distinctly separate force. It can be added to the list of forces (along with tension, friction, normal, etc.) that might act upon an object.
Calculations
1. What is the net force acting on a 5.0 kg object that has a velocity of 15 m/s and is moving in a circle of radius 1.6m?
2. What is the net force acting on a 52 kg object that has a velocity of 17 m/s and is moving in a circle of radius 1.6m?
3. In the display window of the toy store at the local mall, a battery-powered plane is suspended from a string and flying in a horizontal circle. The 631-gram plane makes a complete circle every 2.15 seconds. The radius of the circle is 0.950 m. Determine the velocity of, acceleration of, and net force acting upon the plane.
4. Dominic is the star discus thrower on South's varsity track and field team. In last year's regional competition, Dominic whirled the 1.6 kg discus in a circle with a radius of 1.1 m, ultimately reaching a speed of 52 m/s before launch. Determine the net force acting upon the discus in the moments before launch.
5. Landon and Jocelyn are partners in pair figure skating. Last weekend, they perfected the death spiral element for inclusion in their upcoming competition. During this maneuver, Landon holds Jocelyn by the hand and swings her in a circle while she maintains her blades on the ice, stretched out in a nearly horizontal orientation. Determine the net force which must be applied to Jocelyn (m=51 kg) if her center of mass rotates in a circle with a radius of 61 cm once every 1.9 seconds.
6. A 900-kg car moving at 10 m/s takes a turn around a circle with a radius of 25.0 m. Determine the acceleration and the net force acting upon the car.
7. Determine the centripetal force acting upon a 40-kg child who makes 10 revolutions around the Cliffhanger in 29.3 seconds. The radius of the barrel is 2.90 meters.
8. The mass of a sled and its two riders is 350 kg. Find the magnitude of centripetal force that acts on the sled during a turn with a radius of 33 m and 24 m if the velocity of the sled is 34 m/s.
9. You are spinning a 0.15 kg yo-yo with a velocity of 4 m/s. What is the centripetal force if the yo-yo string is o.8 m long?
10. It takes a 900. kg racing car 12.3 s to travel at a uniform speed around a circular racetrack of radius 90.0 m. What is the centripetal force acting on the car, and which force provides it?
Answers – Concepts
Review Questions:
1. The net force acting upon an object is ___in the same direction___ as the direction of the object's acceleration.
a. in the same direction b. in the opposite direction
c. ... nonsense! There is no simple rule which relates the direction of the a and Fnet vectors.
2. Consider the top view of the clockwise motion of an object shown at the right. Draw an arrow to indicate the direction of the ...a. acceleration vector at location A.
b. velocity vector at location C.
c. velocity vector at location D.
Label your arrows with an a (for acceleration) and a v (for velocity).
The acceleration vector should be directed inwards; the velocity vector should be directed tangent to the circle. /
Force Analysis of Circular Motion:
Every instance of the motion of an object in a circle or along a circular turn involves some force that is directed inward or centripetally. The centripetal force is an adjective to describe the net force; it is not actually a new force to be added to an already lengthy list - including friction, gravity, applied, tension, normal, spring, air resistance, etc. Rather, the centripetal force requirement is a principle that states that in order to have the motion of an object in a circle, there must be an inward net force to sustain the inward acceleration.
3. In each of the following instances, identify the type of the force that fulfills the centripetal force requirement. That is, identify the inward force acting upon the bold-faced object.
Description of a Circular-Type Motion / Centripetal Forcea. A planet is orbiting the sun. / Gravity Force
b. A bucket (filled with water) is held by a string and whirled in a horizontal circle. / Tension Force
(supplied by string)
c. Passengers on the CliffHanger amusement park ride (a barrel ride) are rotated rapidly in a circle. / Normal Force
(supplied by wall)
d. The moon is orbiting the Earth. / Gravity Force
e. A car is making a turn along a level roadway. / Friction Force
f. A car is making a turn along a banked exit ramp. / Friction and Normal Force
g. In football, a halfback leans in and rounds the corner to head up field. / Friction Force
(supplied by ground)
h. A roller coaster car is at the top of a circular loop (on the inside of the track). / Gravity and Normal Force
i. A roller coaster car is at the bottom of a circular loop (on the inside of the track). / Normal Force
j. Clothes move in a circle during the spin cycle in a washing machine. / Normal Force
(supplied by wall of barrel)
4. Consider the diagram in question #2 on the front side. Draw an arrow on the diagram to indicate the direction of the net force vector at both locations B and E. Label the vector with an F (for force).
5. Consider a roller coaster car passing through a clothoid loop. Two strategic positions on the loop are the top and the bottom of the loop. In the diagrams below, draw force vectors on the riders to depict the direction and the magnitude of the two forces acting upon the riders. The size of the force should be approximately equal to the size of the vector arrow. Label the two arrows according to type - Fgrav and Fnorm.
6. When the roller coaster car is at the bottom of the loop, the direction of the acceleration and the net force is directed __up__ (up, down). When the roller coaster car is at the top of the loop, the direction of the acceleration and the net force is directed __down__ (up, down).
7. In order for the conditions described in question #6 above to be true, how does the magnitude of the normal force compare to the magnitude of the gravity force at the two locations. Put a greater than (>) or a less than (<) symbol in the blanks below.
Loop Bottom: Fnorm Fgrav Loop Top: Fnorm ??? Fgrav
(The normal force must be greater than the gravity force when the rider is at the bottom of the loop. This is necessary because there MUST BE a net force upwards - i.e., towards the curve's center. Since the Fgrav is directed ouward, the Fnorm must overwhelm it to produce an upward Fnet. At the top of the loop, the net force must be downward -i.e., towards the curve's center. Since the gravity force is directed downward, there is no need for the normal force at the top of the loop to be a given size. )
8. A person's sensation of weight is due to the presence of a normal force upon their body. Usually, this normal force is of the same magnitude as the force of gravity. So a 600 Newton person typically feels 600 N of normal force to provide a sensation of how much they weigh. When the normal force becomes greater than or less than the force of gravity, a person has a sensation of feeling heavy or feeling light. Where on the roller coaster loop would a person most likely feel heavy - top or bottom? ___Bottom of Loop___ Explain your answer.
Since the normal force is what gives a person a sensation of their weight, the feeling of heaviness will be greates wherever the normal force is greatest. As shown in the free-body diagram (question #5) and explained in question 7, the normal force is greatest at the bottom of the loop. At the llop bottom, the normal force must be greater than Fgrav, thus providing the heavy sensation.
9. TRUE or FALSE:
The centripetal force is a distinctly separate force. It can be added to the list of forces (along with tension, friction, normal, etc.) that might act upon an object.
False! Centripetal is simply an adjective that describes the direction of the net force. This net force can be supplied by any force or combination of forces, but it must be centripetal or directed towards the center of the circle for any object moving along a curved or circular path.
Answers Calculations
1) 705 N
2) 9393 N
3) velocity: 2.78 m/s acceleration: 8.11 m/s/s net force: 5.12 N
4) 3.9 x 103 N
5) 340 N
6) a = 4 m/s2 Fnet = 3600 N
7) 533.4 N
8) 1,261 N and 16,858 N
9) 3N
Academic Physics – Anderson High School 2013 Page 3