MMP Chapters 3,4, and 5
A BMX bicycle rider takes off from a ramp at a point 1.8 m above the ground. The ramp is angled at 40∘∘ from the horizontal, and the rider's speed is 5.9 m/s when he leaves the ramp.
5 m
If Emily throws the ball at an angle of 30∘∘ below the horizontal with a speed of 12m/s, how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 4.0m
5 m
Riders on the Power Tower are launched skyward with an acceleration of 4g, after which they experience a period of free fall What is a 60 kg rider's apparent weight during the launch? What is a 60 kg rider's apparent weight during the period of free fall?
- 2940 N - 0
Corey, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 NN for the first 3.0 s after the elevator starts to move, then 930 NN for the next 3.0 s. What is the elevator's velocity 6.0 s after starting?
- 3. 2 m/s negative because it is a downward motion
Just after vertical launch from Earth surface, the space shuttle takes 8.0 s to reach a speed of 160 km/h During this phase, what is the apparent weight of a 90 kg astronaut?
1,383 N
For typical rubber-on-concrete friction, what is the shortest time in which a car could accelerate from 0 to 70 mph? Suppose that μs=1.00 and μk=0.80μk
3.2 s
How much horizontal force FF must a sprinter of mass 64 kg exert on the starting blocks to produce this acceleration?
960 N
The rope can support a maximum tension of 8300 NN . Is this rope strong enough to do the job? Choose the correct answer and explanation.
No. The tension in the ropes exceeds the maximum value, the ropes will break. Here we learn how to estimate if the rope is strong enough to support the beam given the tension in the rope and its maximum allowable tension.
If the initial speed of the pumpkin is doubled, how does the maximum height change? (Note: for this part, as well as later parts, you will need to use the zoom in and out buttons to see the full trajectories)
The maximum height would increase by four
So far in this tutorial, you have been launching a pumpkin. Let's see what happens to the trajectory if you launch something bigger and heavier, like a car. Compare the trajectory and range of the pumpkin to that of the car, using the same initial speed and angle (e.g., 45∘). (Be sure that air resistance is still turned off.) Which statement is true?
The trajectories and thus the range of the car and the pumpkin are identical.
In the sport of parasailing, a person is attached to a rope being pulled by a boat while hanging from a parachute-like sail. A rider is towed at a constant speed by a rope that is at an angle of 13 ∘∘ from horizontal. The tension in the rope is 1500 NN. The force of the sail on the rider is 30∘∘ from horizontal
w = 510 N
Suppose you hit a 0.058-kgkg tennis ball so that the ball then moves with an acceleration of 10 m/s2m/s2. If you were to hit a basketball of mass 0.58 kgkg with the same force, what would the acceleration aaa of the basketball be?
1 m/s/s
Find the x- and y-components of the vector d = (4.0 km , 30 ∘left of +y-axis). Express your answer in kilometers. Enter the x and y components of the vector separated by a comma.
-2.0,3.5 km
What is the maximum value the string tension can have before the can slips? The coefficient of static friction between the can and the ground is 0.44.
12.3 N
The acceleration of a baseball pitcher's hand as he delivers a pitch is extreme. For a professional player, this acceleration phase lasts only 50 msms, during which the ball's speed increases from 0 to about 90 mphmph, or 40 m/sm/s. What is the force of the pitcher's hand on the 0.145 kgkg ball during this acceleration phase?
120 N
Trained dolphins are capable of a vertical leap of 7.0 m straight up from the surface of the water-an impressive feat.Suppose you could train a dolphin to launch itself out of the water at this same speed but at an angle.
14 m
If the bird's mass is 97 gg, what is the maximum net vertical force exerted on the bird?
2.4 N
If you were to hit a Ping Pong ball of mass 0.0029 gg with the same force that caused a 0.058-gg tennis ball to move with an acceleration of 10 m/s2m/s2 , what would the acceleration aaa of the Ping Pong ball be?
200 m/s/s
A peregrine falcon in a tight, circular turn can attain a centripetal acceleration 1.5 times the free-fall acceleration. If the falcon is flying at 20 m/s , what is the radius of the turn?
27.21 m
A ball thrown horizontally at viviv_i = 21.0 m/sm/s travels a horizontal distance of ddd = 51.0 mm before hitting the ground. From what height hhh was the ball thrown?
28.9 m
The Lamborghini Huracan has an initial acceleration of 0.85gg. Its mass, with a driver, is 1510 kg. If an 80 kg passenger rode along, what would the car's acceleration be?
7.91 m/s/s
When the pumpkin is shot straight upward with an initial speed of 14 m/s, what is the maximum height above its initial location?
9.99 m
The first physicist gets a second physicist to help. They both push on the crate, parallel to the surface of the incline, and it moves at constant speed up the incline. How does the force exerted by the two physicists on the crate compare with the force of friction on the crate?
Ftwo physicists is greater than Ffriction.
If a squid wished to accelerate up and to the right, in which direction should it eject water?
Down and to the Left
How can you get back to your spacecraft?
Throw the items away from the spaceship.
As she starts to move upward, the student pushes down on the surface with a force that is greater than her weight. What can you say about the net force on her?
The net force is directed upward.
Many birds can attain very high speeds when diving. Using radar, scientists measured the altitude of a barn swallow in a vertical dive; it dropped 208 m in 3.0 s. The mass of the swallow was estimated to be 0.018 kg, and its cross-section area as 5.6×10^−4m^2 What was the drag coefficient for this swallow as it dove?
0.109
A car traveling at 26 m/s runs out of gas while traveling up a 7.0 ∘∘ slope. How far will it coast before starting to roll back down?
283 m
In a crash test, a car is driven into a solid wall at a speed of 35 mph.(Figure 1) shows the car's acceleration as it crashes into the wall. What is the maximum force experienced by the 1890 kg car?
5.7×10^5 N
In the previous part, you found that a pumpkin fired with an initial speed of 22 m/s and an angle of 40∘ reaches the same height as a pumpkin fired vertically with an initial speed of 14 m/s. Which pumpkin takes longer to land?
Both pumpkins are in the air the same amount of time.
You are going sledding with your friends, sliding down a snowy hill. Friction can't be ignored. Riding solo on your sled, you have a certain acceleration. Would the acceleration change if you let a friend ride with you, increasing the mass?
No, increasing the mass does increase the net force on the system but it also increases the inertia. a = Fnetm. Since both the net force and mass are increased, they still cancel leaving the acceleration the same.
An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary, the tension in the cable was 7500 NN. When the craft was lowered or raised at a steady rate, the motion through the water added an 1800 NN drag force. What was the tension in the cable when the craft was being raised from the seafloor?
T = 9300 N
There is a friction force pulling the glasses toward the far edge of the table. Why is there so little motion?
The force acts for a very short time interval, so the change in velocity is very small.
The crate is at rest on the incline. What can you say about the force of friction acting on the crate?
The frictional force points up the incline.
A 2300 kgkg truck has put its front bumper against the rear bumper of a 2500 kgkg SUV to give it a push. With the engine at full power and good tires on good pavement, the maximum forward force on the truck is 18,000 NN. What is the maximum possible acceleration the truck can give the SUV? At this acceleration, what is the force of the SUV's bumper on the truck's bumper?
- 3.8 m/s/s - 9400 N
Anna is running to the right, as shown in (Figure 1). Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anna, both balls are approaching her at the same speed. According to her friends, do the balls have the same speed? According to Anna's friends, which ball was thrown with the faster speed?
- No - Ball One
Identify the forces on the jet
- Normal - Thrust - Weight - Drag
Identify all forces acting on the object.
- Weight - Kinetic friction force - Normal force - Air resistance
Identify the number of the action/reaction pairs of forces between the car and the road surface.
- Weighted and normal - Applied and Friction force
Find the x- and y-components of the vector v→ = (6.0 cm/s , −x-direction).
-6,0
Find the x- and y-components of the vector a→ = (11 m/s2, 38 ∘ left of −y-axis).
-6.8,-8.7 m/s2
Scallops eject water from their shells to provide a thrust force. (Figure 1) shows a smoothed graph of actual data for the initial motion of a 25 gg scallop speeding up to escape a predator. What is the magnitude of net force needed to achieve this motion? How does this force compare to the 0.25 N weight of the scallop?
0.025 N This force is 1/10 of the weight of the scallop.
Suppose you have three objects of equal mass. The first object has a volume of 5 cm3 and is made of a material of density 2 g/cm3. The second object has a volume of 10 cm3cm3 and is made of a material of density 1 g/cm3g. What is the density ρρrho of the material of the third object if its volume is 15 cm3?
0.667 g/cm3
In the winter sport of bobsledding, athletes push their sled along a horizontal ice surface and then hop on the sled as it starts to careen down the steeply sloped track. In one event, the sled reaches a top speed of 9.2 m/s before starting down the initial part of the track, which is sloped downward at an angle of 4.0 ∘∘. What is the sled's speed after it has traveled the first 100 mm?
15 m/s
A student builds a rocket-propelled cart for a science project. Its acceleration is not quite high enough to win a prize, so he uses a larger rocket engine that provides 33% more thrust, although doing so increases the mass of the cart by 15%. By what percentage does the cart's acceleration increase?
16%
If it takes a ball dropped from rest 2.429 ss to fall to the ground, from what height HHH was it released?
28.9 m Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. Because both the ball that was dropped and the ball that was thrown horizontally with an initial speed 21.0 m/sm/s fell the same vertical distance of 28.9 mm , they were in the air for the same amount of time. This result was expected and helps to confirm that you did the calculation in Part D correctly.
To get to his office from home, Greg walks 6 blocks north and then 3 blocks east. After work he meets some friends at a cafe; to get there he walks 3 blocks south and 6 blocks west. All blocks are 660 feet long. What is the straight-line distance from the cafe to his home?
2800 ft
The bird is held in level flight due to the force exerted on it by the air as the bird beats its wings. What is the maximum value of this force due to the air? Note that the bird's weight, the force of gravity acting on it, is calculated using w=mg, a result that will be justified in Chapter 5.
3.4 N
Callisto completes one (circular) orbit of Jupiter in 16.7 days. The distance from Jupiter to Callisto is 1.88×10^9m What is the centripetal acceleration of Callisto?
3.56×10−2 ms2
Now, let's see what happens when the cannon is high above the ground. Click on the cannon, and drag it upward as far as it goes (15 m above the ground). Set the initial velocity to 14 m/s, and fire several pumpkins while varying the angle. For what angle is the range the greatest?
30 degrees
An astronaut's weight on earth is 800 NN. What is his weight on Mars, where g=3.76m/s^2?
310 N
A house painter uses the chair-and-pulley arrangement of (Figure 1) to lift himself up the side of a house. The painter's mass is 60 kg and the chair's mass is 10 kg If the painter is at rest, what is the tension in the rope?
340 N
Erase all the trajectories, and fire the pumpkin vertically again with an initial speed of 14 m/s. As you found earlier, the maximum height is 9.99 m. If the pumpkin isn't fired vertically, but at an angle less than 90∘, it can reach the same maximum height if its initial speed is faster. Set the initial speed to 22 m/s, and find the angle such that the maximum height is roughly the same. Experiment by firing the pumpkin with many different angles. What is this angle?
40 degrees
he range is the horizontal distance from the cannon when the pumpkin hits the ground. This distance is given by the product of the horizontal velocity (which is constant) and the amount of time the pumpkin is in the air (which is determined by the vertical component of the initial velocity, as you just discovered). Set the initial speed to 14 m/s, and fire the pumpkin several times while varying the angle between the cannon and the horizontal. For which angle is the range a maximum (with the initial speed held constant)?
45 degrees
A 4000 kg truck is parked on a 7.0∘∘ slope. How big is the friction force on the truck?
4800 N
An astronaut lifts off in a rocket from the surface of the moon, where gg = 1.6 m/s^2 What vertical acceleration should his rocket have so that his apparent weight is equal to his true weight on earth?
8.2 m/s/s
A Jeep is stuck in the mud. The driver has a winch that can pull on its cable with a force of 40,000 NN. The driver loops the cable through a pulley attached to a tree, then attaches the end of the cable to his Jeep, as shown in (Figure 1). What is the magnitude of the maximum force that can be exerted on the Jeep by this cable arrangement?
80,000 N
A cannon tilted upward at θ = 29 ∘∘ fires a cannonball with a speed of 94 m/s . At that instant, what is the component of the cannonball's velocity parallel to the ground?
82 m/s/s
A simple model shows how drawing a bow across a violin string causes the string to vibrate. As the bow moves across the string, static friction between the bow and the string pulls the string along with the bow. At some point, the tension pulling the string back exceeds the maximum static friction force and the string snaps back. This process repeats cyclically, causing the string's vibration. Assume the tension in a 0.33-m-long violin string is 50 N, and the coefficient of static friction between the bow and the string is μsμs = 0.80. If the normal force of the bow on the string is 0.75 N, how far can the string be pulled before it slips if the string is bowed at its center?
9.9 X 10^-4
While the ball is moving through the air, the horizontal component of the ball's velocity ____________.
Has a constant magnitude
A 1500 kgkg steel beam is supported by the two ropes shown in (Figure 1). Calculate the tension in the rope.
T = 8500 NN
Which body exerts the force that propels the sprinter, the blocks or the sprinter?
The blocks
Think about what subsequently happens to the ketchup, which is initially at rest, and use Newton's first law to explain why this technique is so successful.
The inertia of the ketchup will keep it from moving if it isn't too tightly adhered to the sides of the moving bottle.
How does the range of the pumpkin change if its initial velocity is tripled (keeping the angle fixed and less than 90∘?
The pumpkins range is nine times as far
In the previous part, you discovered that the trajectory of an object does not depend on the object's size or mass. But if you have ever seen a parachutist or a feather falling, you know this isn't really true. That is because we have been neglecting air resistance, and we will now study its effects here. For the following parts, select the "Lab" mode of the simulation found at the bottom of the screen. Notice that you can adjust the mass and diameter of the object being launched. Turn on Air Resistance by checking the box. Fire a cannonball with an initial speed of 18 m/s and an angle of 45∘. Compare the trajectory to the case without air resistance. How do the trajectories differ?
The trajectory with air resistance has a shorter range.
Which of the following statements best sums up the central lesson of this video?
When you push down on a surface, you compress the surface, leading to an upward force from the surface that pushes you upward.
In the 2016 Olympics in Rio, after the 50 mm freestyle competition, a problem with the pool was found. In lane 1 there was a gentle 1.2 cm/s current flowing in the direction that the swimmers were going, while in lane 8 there was a current of the same speed but directed opposite to the swimmers' direction. Suppose a swimmer could swim the 50.0 m in 25.0 s in the absence of any current. How would the time it took the swimmer to swim 50.0 m change in lane 1? How would the time it took the swimmer to swim 50.0 m change in lane 8? How does the difference in these times compare to the actual 0.06 ss difference in times between the gold medal winner and the fourth-place finisher?
- 0.15 s - 0.15 s - The difference between the actual results is less than the hypothetical calculated difference
A ball with a horizontal speed of 1.25 m/s rolls off a bench 1.00 m above the floor. How long will it take the ball to hit the floor? How far from a point on the floor directly below the edge of the bench will the ball land?
- 0.452 s - 0.564 m
An impala is an African antelope capable of a remarkable vertical leap. In one recorded leap, a 45 kg impala went into a deep crouch, pushed straight up for 0.21 s, and reached a height of 2.5 m above the ground. To achieve this vertical leap, with what force did the impala push down on the ground? What is the ratio of this force to the antelope's weight?
- 1939.5 N - 4.40
In rock climbing, various rope and pulley systems have been devised to help haul up heavy loads, including injured climbers. A rescuer is hauling up an injured climber who weighs 840 N using the rope and pulley system shown in (Figure 1). (The ropes in this figure are drawn at various angles for clarity, but you can assume they're all vertical.) What is the tension in rope 1, the rope that the rescuer pulls on? What is the tension in rope 2?
- 280 N - 560 N
What is the static friction force acting on a mountain goat that weighs 850 NN and is standing on such a slope?
- 430 N - 740 N
Anita is running to the right at 5.0 m/s , as shown in the figure. Balls 1 and 2 thrown toward her at 10 m/s by friends standing on the ground.(Figure 1) According to Anita, what is the speed of the first ball? According to Anita, what is the speed of the second ball?
- 5 - 15 m/s
Blocks with masses of 3.0 kg, 4.0 kg, and 5.0 kg are lined up in a row on a frictionless table. All three are pushed forward by a 12 NN force applied to the 3.0 kg block. How much force does the 4.0 kg block exert on the 5.0 kg block? How much force does the 4.0 kg block exert on the 3.0 kg block?
- 5 N - 9 N
Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a 60 kg runner completes a 5.0 km race in 22 minutes. Determine the drag force on the runner during the race. Suppose that the cross section area of the runner is 0.72 m^2 What is this force as a fraction of the runner's weight?
- 7.4 N - 1.3×10^−2
A running mountain lion can make a leap 10.0 m long, reaching a maximum height of 3.0 m What is the speed of the mountain lion just as it leaves the ground? At what angle does it leave the ground?
- 9.98 m/s - 50.2 degrees
When setting up projectile motion questions, which of the following characteristics of projectile motion are important to keep in mind?
- Although the horizontal and vertical motions of a projectile are independent, they are connected through the time Δt that the object is in the air. - Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction.
First, you will investigate purely vertical motion. The kinematics equation for vertical motion (ignoring air resistance) is given by y(t)=y0+v0t−(1/2)gt2y(t)=y0+v0t−(1/2)gt2, where y0=0y0=0 is the initial position, v0v0v_0 is the initial speed, and ggg is the acceleration due to gravity. Drag the cannon downwards so it is at ground level, or 0 mm (which represents the initial height of the object), then fire the pumpkin straight upward (at an angle of 90∘90∘) with an initial speed of 14 m/sm/s. How long does it take for the pumpkin to hit the ground?
2.85 s Correct answer is shown. Your answer 2.86s2.86s was either rounded differently or used a different number of significant figures than required for this part. Notice that this value could be determined from the kinematics equation. Given that the initial and final height of the pumpkin is 0 mm, the kinematics equation becomes (v0−0.5gt)=0(v0−0.5gt)=0, or t=2v0/g=2.9 st=2v0/g=2.9 s. This calculation is interesting because it shows that, for vertical motion, the time the pumpkin is in the air is proportional to its initial speed.
A physicist attempts to push the crate up the incline. The physicist senses that if he applies slightly more force the crate will move up the incline but cannot muster enough strength to get the motion started. What can you say now about the force of friction acting on the crate?
A physicist attempts to push the crate up the incline. The physicist senses that if he applies slightly more force the crate will move up the incline but cannot muster enough strength to get the motion started. What can you say now about the force of friction acting on the crate?
Which of the following describes how aaa and mmm are related in the previous two parts?
As mmm shrinks to zero, aaa grows toward infinity. As mmm grows toward infinity, aaa shrinks to zero.
What happens to the trajectory of the cannonball when you increase the diameter while keeping the mass constant?
Increasing the size makes the range of the trajectory decrease.
Can you identify the force that is pushing you back?
No, there is no force pushing you backward, just the seat pushing fo
An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary, the tension in the cable was 7500 NN. When the craft was lowered or raised at a steady rate, the motion through the water added an 1800 NN drag force. What was the tension in the cable when the craft was being lowered to the seafloor?
T = 5700 N
A cart that is rolling at a constant velocity on a level table fires a ball straight up out of a vertical tube. When the ball comes back down, where will it land? Does your answer change if the cart is accelerating in the forward direction? If so, how?
The ball will land directly into the tube. The answer changes: the ball will land behind the tube.
You might think that it is never a good approximation to ignore air resistance. However, often it is. Fire the cannonball without air resistance, and then fire it with air resistance (same angle and initial speed). Then, adjust the mass of the cannonball (increase it and decrease it) and see what happens to the trajectory. Don't change the diameter. When does the range with air resistance approach the range without air resistance?
The range with air resistance approaches the range without air resistance as the mass of the cannonball is increased.
Which of the following statements best sums up the central lesson of this video?
The vertical motion of a projectile is independent of its horizontal motion.
When the tablecloth is pulled over the far edge of the table, which way will the glassware move?
Toward the far edge of the table.
