HSC 216 Exam 2 practice questions
A 0.43 kg soccer ball is stationary on the field when Daryl kicks it. Daryl's foot is in contact with the ball for 0.01 s during the kick. The horizontal velocity of the ball as it leaves his foot is 25 m/s. What is the average horizontal force exerted by Daryl's foot on the ball during the contact period? (assume 0 friction)
1,075 N Response Feedback: F*t = m* (vf-vi) F = (m (vf - vi))/ t F = (.43 (25-0))/ .01 F = 1,075 N
A gymnast falls from the high bar and lands on a 10 cm thick mat. The gymnast strikes the back of his head against the mat in the landing. His head is moving at 7 m/s when it first strikes the mat. The mass of the head is 5 kg. The impact ends when the gymnast's head comes to a stop after deflecting the mat 6.5 cm. How much kinetic enregy does the gymnanst's head have the instant it strikes the mat?
122.5 J Response Feedback: KE = 1/2 m*v^2 KE = 1/2 (5)*(7^2) KE = 122.5 J
What is the average angular velocity of an object moving through 30° in 2 s?
15° per second
A net horizontal force of 200 N is applied to a wrestler of mass 100 kg. The horizontal acceleration of the wrestler will be
2 m/s2
What is the net torque when you are holding a 10 lb weight 1 ft from your elbow (producing a clockwise torque) and your biceps is generating a 50 lb force with a moment arm of 3 in. (producing a counterclockwise torque)?
2.5 ft·lb
Why is a second-class lever well adapted to moving heavy loads?
The effort arm is longer than the resistance arm A second class lever has the resistance between the axis and effort. This means the effort arm will be longer than the resistance arm so if the same ammount of force is applied to both, the effort would cause more torque
In the kinetic energy equation, which component is most important?
velocity
Which of the following is not a unit of angular displacement?
watt (power) radian, revolution and degree are angular displacement
Define "moment arm"
The perpindicular distance from the axis of rotation of a lever to the line of an applied force
Barbara is standing still (velocity = 0) when her skating partner, Paul, begins to lift her up and throw her into the air. Barbara's mass is 70 kg. Pauls exerts an average vertical force of 800 N for 1.0 s on Barbara during the lifting movement. Use the impulse-momentum relationship to find Barbara's vertical velocity when Paul releases her?
ΣF*t = m*(vf-vi) ΣF = Force throw + force weight ΣF = 800 + (-9.81*70) ΣF = 113.3 N 113.3*1 = 70*(vf-0) 113.3/ 70 = vf vf = 1.62 m/s
During a drive by golfer Tiger Woods, the angular velocity of his club is zero at the top of the backswing and 30 rad/s at the bottom of the downswing just before impact with the ball. If the downswing lasts 0.30 s, what is the average angular acceleration of the club during the downswing?
α = (ωf- ωi)/t α = (30- 0)/0.3 α = 100 rad/s
At full knee extension, the relative angle between the lower leg and thigh is 178 degrees. At full flexion, it is 82 degrees. What is the total angular displacement demonstrated in radians?
θ = (θf - θi) θ = (178 - 82) θ = 96° θ = 96° * (1 rad/ 57.3°) θ = 1.68 radians
For a body to be in static equilibrium,
all forces acting on the body must sum to zero all torques acting on the body must sum to zero the body must be stationary Correct all of the above
Strain energy is the energy
due to deformation
Kinetic energy is the energy
due to motion
If the velocity of a runner changes from -2 m/s to -4 m/s over a period of time, the runner's kinetic energy will become
four times as great as it was
How long would a lever be if a change in angle of 1.92 radians resulted in an arc length of 3.07 meters?
l = Θ * r r = l / Θ r = 3.07 / 1.92 r = 1.60 meters
In the average female, the center of gravity is located
lower than in the average male
If a net horizontal force is applied to a body that is moving horizontally, the body will
need more information to determine
Stability may be increased by
raising the center of mass decreasing the number of contact points in the base of support widening the base of support perpendicular to any oncoming force leaning away from an oncoming force Correct none of the above
In the equation for calculating strain energy, the x symbolizes
the amount of deformation
If a body of constant mass is traveling with a constant velocity,
there must be no net force acting on the body
Doris is trying to life a stack of heavy books off a table. The books have a mass of 15 kg. What is the minimum vertical force she much exert on the books to lift the books off the table?
ΣF > 0 ΣF = Fp + Fg Fp + (15*-9.81) > 0 Fp > 0 - (-147.15) Fp > 147.15 N
A 3.0 meter seesaw of uniform mass is pivoted 1.5 m from the end. A 35 kg child sits 0.6 meters from the pivot. How far on the opposite side of the pivot must a 20 kg child sit in order for the beam to be in equilibrium (assuming the seesaw is in line with the horizontal plane)?
-1.05 meters from the axis of rotation Response Feedback: Torque caused by child A (35kg child) T = F*d┴ T = (35*-9.81) * 0.6 T = -343.35 * 0.6 T = -206.0 N*m Torque caused by child B ΣT = 0 (Equilibrium) TA = -TB -206.0 = -(-206.0) TB = 206.0 N*m Moment arm of child B T = F*d┴ d┴ = T/F d┴ = 206.0/ (20*-9.81) d┴ = -1.05 meters from the axis of rotation Note: Negative torque indicates a torque that will cause rotation opposite the rotation of the child we care about. A negative moment arm indicates the moment arm is in the opposite direction from the axis of rotation as the other AOR (this only comes into play with this type of lever).
A 60 kg gymnast hold an iron cross position on the rings. In this position, the gymnast's arms are abducted 90 degrees and his trunk and legs are vertical. The horizontal distance from each ring to the gymnast's nearest shoulder is 0.60 m. The gymnast is in static equilibrium. How much torque must the right shoulder adductor muscles produce to maintain the iron cross position?
-176.6 N*m a) ΣF = 0 FR = -Fg FR = -(60*-9.81) FR = 588.6 N / 2 hands FR1/2 = 294.3 N b) TR = F*d┴ TR = 294.3 * 0.6 TR = 176.6 N*m c) ΣT = 0 TR = -TE TE = -176.6 N*m
In a vertical jump test, 60 kg Tracy jumps 60 cm, while a 90 kg Paul jumps 45 cm. Assuming both jumps take the same amount of time, which jumper was more powerful?
. Paul
A 600 N volleyball player lands from a spike attempt and immediately jumps up to try for a block. When she first contacts the ground, her velocity is 3 m/s downward, and then as she leaves the ground for the block her velocity is 4 m/s upward. Her kinetic energy at maximum knee flexion (i.e., at the end of landing, when her vertical velocity is 0 m/s) is
0 J KE = 1/2 m*v^2 Velocity at this point is zero, so KE would also be zero
Katherine is attempting a biceps curl with a 100N dumbbell. She is standing upright and her forearm is horizontal.The moment arm of the dumbbell about Katherine's elbow joint is 30 cm. Ignore the weight of Katherine's arm and hand. If Katherine's elbow flexor muscles contract with a force of 1000N and hold the dumbbell in static equilibrium, what is the moment arm of the elbow flexor muscles about the elbow joint?
0.03 meters Response Feedback: a) T = F*d┴ T= 100*.3 T= 30 N*m b) Hold in this position = Static Equilibrium ΣT = 0 TR + TE = 0 TE = -TR TE = -30 N*m c) T = F*d┴ T/F = d┴ d┴ = -30 / -1000 d┴ = .03 meters Note: Force is negative because it acts opposite the force of the dumbbell, which was positive.
If you lift up on the 25 kg bag with 275 N of vertical force, the acceleration of the bag will be
1 m/s2
What is the torque if a 50 N force is applied 2 m from the axis of rotation?
100 Nm
A bicycle has a kinetic energy of 124 J. What kinetic energy would the bicycle have if it three times the mass and moving one-half the speed?
124 = .5mv2 124 = .5(3m)(1/2v)2 124 = .5 (3m) (1/4v2) 124 = ¾ (.5mv2) Factor of ¾ increase so 93 J
Sasha Cohen does a triple toe loop and rotates three times around in 1 s. What is her average angular speed during this jump?
3 rev/s
A gymnast falls from the high bar and lands on a 10 cm thick mat. The gymnast strikes the back of his head against the mat in the landing. His head is moving at 7 m/s when it first strikes the mat. The mass of the head is 5 kg. The impact ends when the gymnast's head comes to a stop after deflecting the mat 6.5 cm. What is the net change in potential energy of the gymnast's head when it strikes the mat?
3.19 J Response Feedback: PE = mgh PE = 5*9.81*0.065 PE = 3.19 J
Zoe is pole-vaulting. At the end of her approach run, she has a horizontal velocity of 8 m/s and her center of gravity of 1.0 m high. If Zoe's mass is 50 kg, estimate how high she should be able to vault if her kinetic and potential energies are all converted to potential energies?
4.26 meters above the ground
During a golf drive, the angular velocity of the driver is 20 rad/s just before impact with the golf ball. If the distance from the club head to the axis of rotation is 2.0 m, what is the linear velocity of the club head?
40 m/s
What is the gravitational potential energy of a circus performer with a mass of 50 kg walking on a tightrope 10 m above the ground?
4905 Nm
If the moment arm is 5 cm, and the force is 100 N, the magnitude of the torque will be
5 Nm
A garbage collector routinely has to pick up trash bags and toss them into the back of the waiting truck. The collector must lift the bag of garbage from the curb, and then lift it up and throw it into the back of the truck. If the average bag of garbage has a mass of 10 kg and the collector can apply a vertical force of 150 N for 1.25 seconds, what is the bag's vertical velocity when the collector releases the bag?
6.5 m/s ΣF*t = m*(vf-vi) ΣF= force lift + weight ΣF= 150 + (-9.81*10) ΣF= 51.9 N ΣF*t = m*(vf-vi) 51.9*1.25 = 10*(vf-0) (51.9*1.25)/10 = vf vf = 6.49 m/s
Define Torque
A component of a force that acts perpindicular to a lever arm and causes rotation to occur mutiplied by the lever length to that component force. Torque is the rotational component of a force.
When a vollyball player uses the court to propel herself above the net for a block, which of Newton's laws is best represented by the interaction of the volleyball player and the floor?
Action Reaction Response Feedback: The best answer is Newton's third law, Action Reaction, because she applies a force on the floor enough that the floor will push her back above the net.
As a bowler rolls the ball, his shoulder travels from 90 degrees of hyperextension to 70 degrees of flexion in 0.90 seconds. Was the average angular velocity of his arm during the attempt?
Angle (Assume neutral = 0 degrees so hyperextension is (-) and flexion is (+): θ = (θf - θi) -90 - 70 = -160° -160° * (1 rad/ 57.3°) = 2.79 rad ω = (θf - θi)/t ω = 2.79/0.9 ω = 3.1 rad/s
Bill lifts a 900 N barbell 1.5 m in 1.0 s, while Bob lifts a 1400 N barbell 2.0 m in 2.0 s. Whose lift is more powerful?
Bob's P = W/t W = F*d Bill W = 900*1.5 W = 1,350 J P = 1,350/ 1 P = 1,350 W Bob W = 1,400* 2 W = 2,800 J P = 2,800/ 2 P = 1,400 W
A person performs a bench press. The bar's mass is 50 kg. When this person's arms are extended, the bar is 0.6 m above the starting point. If the man does 600J of work, how much average force did he apply to the bar?
Correct 1,000 N W = F*d F= W/d F= 600/ 0.6 F= 1,000N
What happens to your center of gravity when you add a 200 N suitcase to your hand held out to your side?
Correct The center of gravity shifts in the direction of the suitcase.
At the top of a giant swing on the gymnastics high bar, the gymnast's velocity is 1 m/s and she is 3.5 m high. If she has a mass of 50 kg , what is her total mechanical energy at this instant?
D. 1741.8 J Response Feedback: ET = PE + KE ET = mgh + 0.5m*v2 ET = 50*9.81*3.5 + .5*50*12 ET = 1716.75 + 25 ET = 1741.8 J
During the delivary phase of a fastball pitch, the arm internally rotates at the shoulder joint. The angular velocity of this internal rotation peaks at 67 rad/s. If the distance from the shoulder joint to the hand is .45 meters. What is the tangential velocity of the ball at this angular velocity?
D. 30.2 m/s Response Feedback: vt = ω*r vt = 67*0.45 vt = 30.2 m/s
During an arm wrestling match, your opponent is winning. She is slowly pushing your arm down toward the table. If you are doing any mechanical work against your opponent, the work is
Direction of force of you on them = (+) Direction of their arm moving = (-) So you would be performing negative work
The moment arm of the biceps brachii muscle about the elbow joint is largest when the angle at the elbow joint is approximately
Feedback: At 90 degrees, there should be the greatest distance from the insertion point of the muscle to the axis of rotation, so the line of pull of the muscle will most likely have the largest moment arm.
A child tries to swing an adult size baseball bat without choking up on it. She can manage only 200 deg/s of angular velocity with a radius of 80 cm. But then she chokes up on the bat thereby reducing the radius of rotation by 10 cm. She can now generate an angular velocity of 300 deg/s. Compute the linear velocity of the endpoint of the bat in each case in m/s (watch your units!).
First attempt: 2.7 m/s Second attempt: 3.7 m/s Swing 1 vt = ω*r vt = (200/57.3) * 0.8 vt = 2.7 m/s Swing 2 vt = ω*r vt = (300/57.3)*0.7 vt = 3.7 m/s
As the mass of an object increases, what happens to its inertia?
It increases
If you increase the time during which a constant force is applied to an object, what effect does this have on the impulse given to the object?
It increases the impulse.
Ima Scarred (m=56.2 kg) is traveling at a speed of 6.8 m/s at the top of a 9.5-m high roller coaster loop. Determine Ima's speed at the bottom of the loopa.
KE= .5mv2 KE= .5 (56.2) 6.82 KE= 1,299.3 J b) PE = mgh PE = 56.2*9.81*9.5 PE= 5,237.6 J c) Ei = Ef PEi + KEi = Ef 5,237.6 + 1,299.3 = 6536.9 J d) Ef = PE + KE Ef = mgh + .5mv2 (Ef - mgh / .5m)1/2 = v v = [6536.9 - (56.2*9.81*0) / .5*56.2]1/2 v = (6536.9/28.1)1/2 v= 15.3 m/s
If the person to the right is using a 100N dumbbell and as a forearm that is 0.3 m long, how much torque does the dumbbell cause about the elbow when the forearm is 30 degrees above the horizontal?
Note: Weight acts straight down, so the perpindicular distance to the line of the weight (moment arm of the weight) will be the horizontal plane from the axis of rotation to directly under the weight. This will be the horizontal piece of the lever length at that angle. cos θ = adjacent/ hypotenuse cos 30 = adjacent/ 0.3 adjacent = 0.3 cos 30 adjacent = 0.26 meters Torque = F* d┴ Torque = 1000* 0.26 T= 26 N*m
Two nurses bend to lift a patient from the floor. The patient weights 90 kg and the distance between the center of mass of the patient Nurse A and Nurse B's axis of rotation is 0.8 meters horizontally. However, Nurse A, who's head, arms and trunk (HAT) weigh 190N, bends her knees so her HAT center of mass is directly above her axis of rotation, while nurse B, who's HAT also weigh 190N, bends at her hips only, causing the center of mass of her HAT to be 0.2 meter away from her axis of rotation, horizontally. What magnitude of torque will each nurse have to generate to lift the patient from the floor? Hint: Try to draw this. Remember, each nurse will be lifting only half the patient's bodyweight.
Nurse A: >353.2 N*m, Nurse B: > 391.2 N*m Nurse A ΣT = T lift + T hat ΣT = F* d┴ + F* d┴ ΣT = 441.5* 0.8 + 190 * 0 ΣT = 353.2 N*m Nurse B ΣT = T lift + T hat ΣT = F* d┴ + F* d┴ ΣT = 441.5* 0.8 + 190* 0.2 ΣT = 391.2
A 25 kg child climbs two steps of 20 cm each in 2 s. The minimum power generated is
P = W/t W = F*d W = (>Fg)*d W = >245.3*0.4 W = 98.1 J P = 98.1/ (0.2*2) P = >24.5 W P =
The Achilles tendon insets on the calcaneus 8 cm from the axis of rotation of the ankle joint. If the force generated by the muscles attached to the Achilles tendon is 3000N and the moment arm of the force about the ankle joint is 5 cm, what is the torque created by these muscles about the ankle joint?
T = F*d┴ T = 3000 N* .05m T = 150 N*m
If the length of a man's arm is 0.8 m from shoulder to hand, how much torque would a 8kg dumbbell cause on the shoulder if the arm is abducted at an angle of 65° below the horizontal?
T = F*d┴ d┴ = 0.8 cos(65) d┴ = .34 meters T = F*d┴ T = (8*-9.81)*.34 T = -26.7 N*m
On a rigid segment that is undergoing angular motion, which of the following statements is true?
The angular displacement of any two points on the segment would be equal.
For a rotating object, the acceleration directed toward the center of rotation is called
The centripetal acceleration
A 75 kg jumper lands stiff-legged on the floor and changes his velocity from -4.5 m/s to zero in 0.15 seconds. Compute the average ground reaction force under his feet during this time interval. If he increased the impact time to 0.2 s, what happens to the ground reaction force?
The ground reaction force will be lower in the second jump (0.2 seconds). Jump 1 F*t = m* (vf-vi) F= m* (vf-vi) / t F= 75* (0 - (-4.5)) / .15 F= 2250 N Jump 2 F*t = m* (vf-vi) F= m* (vf-vi) / t F= 75* (0 - (-4.5)) / .2 F= 1687.5 N 2250 N > 1687.5 N Therefore, increasing the time of impact (the impulse for the GRF in this example) will decrease the GRF.
What is the effort arm in a leg rotating at the knee?
The perpindicular distance from the knee joint to the line of the pull of the quadriceps muscle group Feedback: Effort arm refers to the moment arm of the force that requires an active process to create torque. Resistance arm refers to the moment arm of the force that causes torque passively or outside of the body/ system (like a box sitting on a lever, or the weight of the leg). Since both are moment arms, both will be the perpindicular distance from the axis of rotation (the knee joint) to the line of each force (the pull of the quads for the effort arm; the weight of the leg acting through the center of mass of the leg for the resistance arm).
A 70 kg wide receiver, James, turns and sprints toward the QB at a speed of 9m/s. The QB releases the .25 kg ball, which is traveling -28m/s when James catches it. How fast and in what direction will James and the ball be traveling after the ball is caught?
8.86 m/s in the direction James was traveling prior to catching the ball. m1v1 + m2v2 = (m1+m2)*v (m1v1 + m2v2)/ (m1+m2) = v v= (70*9 + .25*-28) / (70+.25) v= 623/ 70.25 v= 8.86 m/s in the direction James was traveling since it is positive
During the pitching motion, a baseball pitcher exerted an average horizontal force of 80 N against the 0.15 kg baseball while moving it through a horizontal displacement of 2.0 m before release. The amount of work performed by the pitcher on the baseball was
W = F*d W = 80 * 2 W = 160 J
Jill's bocci ball rolls with a velocity of 1 m/s, while Jack's rolls with a velocity of 2 m/s in the same direction. Both balls have the same mass. A 10 N average force stops Jill's ball in a distance of 1 m. How big is the average force required to stop Jack's ball over the same 1 m distance?
W = F*d W = ΔKE + ΔPE W = 1/2 m*v^2 + 0 Mass of the ball W = 1*10 W = 10 10 = 1/2 m* (1^2) m = 20 kg Force W = 1/2 (20) * (2^2) W = 40 J W = F * d F = 40/ 1 F = 40 N
An angle formed between two body segments is an example of
a relative angle
If a net horizontal force is applied to a body that is at rest, the body will
accelerate
An angle formed between a body segment and a horizontal reference line is an example of
an absolute angle
Joe swings a bat from rest and contacts a ball at a speed of 17 rad/s. The swing takes a total of 0.23 seconds. If his arms and the bat form a lever arm with a length of 2.2 meters, what is the radial acceleration at the end of the bat?
ar = ω2 * r ar = 172 * 2.2 ar = 635.8 m/s2
The center of gravity of an object of uniform density is located
at the exact center of the object
The moment arm of the biceps brachii muscle about the elbow joint is largest when the angle at the elbow joint is approximately
90°
By convention, positive angular direction is
counterclockwise
An eccentric force
does not pass through an axis of rotation
Gravitational potential energy is the energy
due to position relative to the earth
If a bag has a mass of 25 kg, how much force must you apply to lift it off a baggage cart?
> 245 N Minimum force > weight therefore minimum force is > mass*gravity >245 N
To start in motion an object sitting at rest on a horizontal surface, the horizontal force applied must be
greater than the vertical force less than the vertical force greater than the weight of the object less than the weight of the object Correct none of the above
Which quantity causes a change in linear momentum?
impulse
An example of using impulse to safely decrease momentum would be
landing on a mat when pole vaulting
If a force acts directly through an object's center of gravity, _______ acceleration will occur.
linear
The product of a force and the time during which the force acts on a body defines
linear impulse
The product of a body's mass and its linear velocity defines
linear momentum
As a joint is moved through its range of motion when strength training with free weights, such as doing the arm curl, the moment arm for the resistance weight will get
longer shorter Correct either a or b
For most segments of the human body, the segmental center of gravity is located
more proximally
The center of gravity of a ring of uniform density is located
outside of the object
A centric force
passes through an axis of rotation
Strain energy is most important in which of the following sports?
pole vaulting
The capacity for doing work that a body possesses because of its position or configuration is known as
potential energy
The form of energy associated with the stiffness and deformability of an object is called
strain energy
The limiting friction between the 25 kg bag and the cart is 50 N. You need to slide the bag to the side of the cart. If you apply 50 N horizontally on the bag,
the bag will remain motionless
The weight of a body is defined as a quantification of the force of gravity acting on which aspect of the body?
Mass Response Feedback: Fg = weight = mass*gravity
An unbelted victim in a car accident will continue to move in the same direction and with the same speed until the dashboard causes a change in motion. This best exemplifies
Newton's first law of motion
When a human body is airborne (e.g., when a person leaps through the air),
the body's center of gravity follows a parabolic flight path movement of the arms and legs will not influence the flight path of the center of gravity air resistance influences the flight path of the center of gravity, but only if the body is moving rapidly Correct all of the above
Gravity can be defined as
the force with which the earth pulls on an object's mass
To determine the length of a moment arm, you would measure
the perpendicular distance from the axis of rotation to the force's line of action
As a football player moves from a two-point stance (standing) to a four-point stance (hands and feet on the ground),
the player's stability is increased
Torque is defined as
the tendency of a force to cause rotation the turning effect of a force the product of force and moment arm Correct all of the above
