Intro to Forces : Two forces acting at a point 2) Two forces, F⃗ 1 and F⃗ 2, act at a point, as shown in the picture. (Figure 1) F⃗ 1 has a magnitude of 9.20 N and is directed at an angle of α = 60.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 6.40 N and is directed at an angle of β = 53.0 ∘ below the negative x-axis in the third quadrant.

no title provided Part A

What is the x component Fx of the resultant force?

Express your answer in newtons.

Fx =

N

Part B

What is the y component Fy of the resultant force?

Express your answer in newtons.

Fy =

N

Part C

What is the magnitude F of the resultant force?

Express your answer in newtons.

F =

N

Part D

What is the angle γ that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

Express your answer in degrees.

γ =

degrees

6)

no title providedAnswer the following questions with reference to the eight forces defined as follows.

· the force of the 3 kg block on the 2 kgblock, F3on2,

· the force of the 2 kg block on the 3 kgblock, F2on3,

· the force of the 3 kg block on the 1 kgblock, F3on1,

· the force of the 1 kg block on the 3 kgblock, F1on3,

· the force of the 2 kg block on the 1 kgblock, F2on1,

· the force of the 1 kg block on the 2 kgblock, F1on2,

· the force of the 1 kg block on the floor, F1onfloor, and

· the force of the floor on the 1 kg block, Fflooron1.

7) Driving home from school one day, you spot a ball rolling out into the street (see the figure (Figure 1) ). You brake for 1.00 s , slowing your 990-kg car from 16.0 m/s to 9.50 m/s.

no title provided Part A

What was the magnitude of the average force exerted on your car during braking?

Express your answer using two significant figures.

F =

N

Part B

What was the direction of the average force exerted on your car during braking?

What was the direction of the average force exerted on your car during braking?

To the direction of motion.

Opposite to the direction of motion.

Part C

How far did you travel while braking?

Δx =

m

9) A train is traveling up a 4.0 ∘ incline at a speed of 3.05 m/s when the last car breaks free and begins to coast without friction

Part A

How long does it take for the last car to come to rest momentarily?

Express your answer using two significant figures.

t =

s

Part B

How far did the last car travel before momentarily coming to rest?

Express your answer using two significant figures.

s =

m

11) At the bow of a ship on a stormy sea, a crewman conducts an experiment by standing on a bathroom scale. In calm waters, the scale reads 185 lb . During the storm, the crewman finds a maximum reading of 220 lb and a minimum reading of 132 lb

Part A

Find the maximum upward acceleration experienced by the crewman.

aup =

m/s2

Part B

Find the maximum downward acceleration experienced by the crewman.

adown =

m/s2

12) Your groceries are in a bag with paper handles. The handles will tear off if a force greater than 49.0 N is applied to them

Part A

What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised with constant speed.

m =

kg

Part B

What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised with an acceleration of 1.50 m/s2 ?

m =

kg

14) Three forces of magnitudes F1=4.0N, F2=6.0N, and F3=8.0N are applied to a block of mass m=2.0kg, initially at rest, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (net) force by combining the three individual force vectors. All angles should be measured counterclockwise from the positive x-axis (i.e., all angles are positive).

no title provided Part A

Calculate the magnitude of the resultant force F⃗ r=F⃗ 1+F⃗ 2+F⃗ 3 acting on the block.

Express the magnitude of the resultant force in newtons to two significant figures.

|F⃗ r| =

N

Part B

What angle does F⃗ r make with the positive x axis?

Express your answer in degrees to two significant figures.

degrees

Part C

What is the magnitude of the block’s acceleration vector, a⃗ ?

Express your answer to two significant figures.

|a⃗ | =

m/s2

Part D

What is the direction of a⃗ ? In other words, what angle does this vector make with respect to the positive x axis?

Express your answer in degrees to two significant figures.

degrees

Part E

How far (in meters) will the block move in 5.0 s? Recall that it starts from rest.

Express the distance d in meters to two significant figures.

d =

m

Chapter 2

5) The two tennis players shown in the figure(Figure 1) walk to the net to congratulate one another

no title provided

Part A

Find the distance traveled and the displacement of player A.

Express your answers using one significant figure separated by a comma.

dA, ΔxA =

m

Part B

Repeat for player B.

Express your answers using one significant figure separated by a comma.

dB, ΔxB =

m

7) A car in stop-and-go traffic starts at rest, moves forward 19 m in 8.0 s, then comes to rest again. The velocity-versus-time plot for this car is given in the figure(Figure 1)

no title provided

Part A

What distance does the car cover in the first 4.0 seconds of its motion?

Express your answer using two significant figures.

d =

m

Part B

What distance does the car cover in the last 2.0 seconds of its motion?

Express your answer using two significant figures.

d =

m

Part C

What is the constant speed V that characterizes the middle portion of its motion?

Express your answer using two significant figures.

V =

m/s

no title provided 9) A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 20.5 m/s , and the distance between them is 52.0 m . After t1 = 5.00 s , the motorcycle starts to accelerate at a rate of 8.00 m/s2 . The motorcycle catches up with the car at some time t2.

Part A

Which of the graphs (Figure 1) correctly displays the positions of the motorcycle and car as functions of time?

Which of the graphs correctly displays the positions of the motorcycle and car as functions of time?

A

B

C

D

E

Part B

How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t2−t1.

Express the time numerically in seconds using three significant figures.

t2−t1 =

s

Part C

How far does the motorcycle travel from the moment it starts to accelerate (at time t1) until it catches up with the car (at time t2)? Should you need to use an answer from a previous part, make sure you use the unrounded value.

Answer numerically in meters using three significant figures.

xm(t2) =

m

10) Ilya and Anya each can run at a speed of 8.00 mph and walk at a speed of 3.10 mph . They set off together on a route of length 5.00 miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.

Part A

How long does it take Anya to cover the distance of 5.00 miles ?

Express your answer numerically, in minutes.

tAnya =

minutes

Part B

Find Anya’s average speed.

Express Anya’s average speed save,Anya numerically, in miles per hour.

save,Anya =

mph

Part C

How long does it take Ilya to cover the distance?

Express the time tIlya taken by Ilya numerically, in minutes.

tIlya =

minutes

Part D

Now find Ilya’s average speed.

Express Ilya’s average speed save,Ilya numerically, in miles per hour.

save,Ilya =

11) The golfer in the figure(Figure 1) sinks the ball in two putts, as shown.

no title provided

Part A

What is the distance traveled by the ball?

Express your answer using two significant figures.

d =

m

Part B

What is the displacement of the ball?

Express your answer using two significant figures.

Δx =

m

12) A finch rides on the back of a Galapagos tortoise, which walks at the stately pace of 0.060 m/s. After 1.5 minutes the finch tires of the tortoise’s slow pace, and takes flight in the same direction for another 1.0 minutes at 12 m/s.

What was the average speed of the finch for this 2.5-minute interval?

Express your answer using two significant figures.

vave =

m/s

14) A rocket blasts off and moves straight upward from the launch pad with constant acceleration. After 2.8 s the rocket is at a height of 82 m .

Part A

What the magnitude of the rocket’s acceleration?

Express your answer using two significant figures.

a =

m/s2

Part B

What is the direction of the rocket’s acceleration?

upward

downward

Part C

What is its speed at this time?

Express your answer using two significant figures.

v =

m/s

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