midterm exam review(physicsi)...midterm exam review(physicsi) testii true or false 1. the length of...

Midterm Exam Review(PhysicsI)

TestII

True or False

1. The length of a vector represents its magnitude ( True False)

2. Speed is the magnitude of velocity ( True False)

3. After an object is thrown into the air at any angle, the only force acting on the object is the gravitational

force. ( True False )

4. The force of gravity is always vertically downward. ( True False )

5. If you throw a ball at any angle with a certain speed, you will catch it at the same speed.

( True False )

6. The horizontal velocity of a projectile thrown at an angle can be affected by the strong force of gravity. (

True False )

7. An object thrown at an angle of 45 degrees will travel further than an object thrown at 40 degrees with

the same initial speed ( True False )

8. An object thrown at a certain angle accelerates in the horizontal direction and also accelerates in the

vertical direction. ( True False )

Multiple Choice

1. Which of the following is a vector quantity?

a) velocity b) speed c) temperature d) mass

2. The horizontal component of a projectile’s velocity is ( )

a) independent of gravity b) changes throughout the motion

c) increases according to time d) independent of the horizontal distance

3. A ball is thrown into the air at some angle. At the very top of the ball’s path, its velocity is

a) entirely vertical b) entirely horizontal c) both vertical and horizontal

d) velocity is zero

4. At what part of a path does a projectile have minimum speed?

a) when it is thrown b) halfway to the top

c) At the top of its path d) right after it passes the top

5. At what part of a path does a projectile have maximum speed?

a) when it is thrown b) halfway to the top

c) At the top of its path d) right after it passes the top

6. An object is thrown into the air at an angle of 60º. When the object is at the maximum height, what is the

angle between the velocity and the horizontal surface?

a) 0º b) 30º c) 60º d) 90º

TestIII True or False

1. The mass of an object is different on Earth compared to the moon ( True False)

2. Force always come in pairs ( True False )

3. Weight and mass is the same quantity ( True False)

4. If you slide an objects on a frictionless surface, there must be a horizontal force on it to keep it in motion

( True False )

5. If an object slides on a frictionless surface, it will eventually slow down ( True False )

Multiple Choice

1. Which object has greater inertia compared to the billiard ball?

a) tennis ball b) volleyball c) bowling ball d) golf-ball

2. A 10N force and a 30N force act on an object in opposite directions. What is the net force on the object?

a) 40N b) 30N c) 20N d) 10N

3. Acceleration is produced by ( )

a) velocity b) acceleration c) force d) mass

4. When an object reaches terminal velocity its acceleration is ( )

a) 10m/s2 b) 6m/s2 c) 2m/s2 d) 0m/s2

5. Suppose the force of friction on a sliding object is 10N. The force needed to maintain a constant velocity

is ( )

a) more than 10N b) less than 10N c) 10N d) 20N

6. Under what condition(s) will an object be in equilibrium(∑F=0)?

a) If it is either at rest or moving with constant velocity

b) If it is either moving with constant velocity or with constant acceleration

c) Only if it is at rest d) Only if it moving with constant velocity

TEST IIA

X-component : x = vx t where vx = v cosθ

Y-component : vyf = vyi – gt y = vyi t - (1/2)gt2 -2gy = vyf 2- vyi

2 where vy= vsinθ

𝒗 = √𝒗𝒙𝟐 + 𝒗𝒚

𝟐

Solve the following questions. (3 pts) You must SHOW your work~! Calculator in degrees!!

1. A ball is thrown horizontally at a height of 14.2 meters with the initial speed of 5.6 m/s. vi=5.6m/s

i) Find the time it takes for the object to hit the surface (Remember that vyi =0 for horizontal projectile

motion)

a) 1.1s b) 1.7s c) 2.5s d) 3.7s

ii) How far did the ball travel?

a) 26.5m b) 21.2m c) 13.9m d) 9.5m

iii) What is the speed the moment the ball hits the ground? ( *~ use vy = - g t and v= √𝑣𝑥2 + 𝑣𝑦

2 )

a) 17.6m/s b) 18.8m/s c) 22.6m/s d) 27.5m/s



2 where vy= vsinθ

𝒗 = √𝒗𝒙𝟐 + 𝒗𝒚

𝟐

2. i) If speed of an object is v=5m/s at a certain point in air, what is the

horizontal component vx?

a) 3.21m/s b) 3.83m/s c) 4.44m/s d) 5.10m/s

ii) Find the vertical component vy.

a) 3.21m/s b) 3.83m/s c) 4.44m/s d) 5.10m/s

v=5m/s

vy

40°

vx

3. A stone is thrown at an angle of 40° to the horizontal and with an initial speed of 10m/s.

x=?

i) Find the time the object is in the air(=total time)

a) 3.2s b) 2.5s d) 1.9s d) 1.3s

ii) Find the maximum height of the stone.

a) 2.1m b) 2.9m c) 3.6m d) 4.9m

iii) Find the approximate horizontal range x of the stone.

a) 10m b) 12m c) 14m d) 16m

iv) What is the maximum speed of the stone?

a) 6.4m/s b) 7.7m/s c) 8.3m/s d) 10m/s

v) Find the minimum speed of the stone

a) 6.4m/s b) 7.7m/s c) 8.3m/s d) 10m/s

Solve the following questions. ( 8points) You must show your work~!Calculator in degrees!!

4. A motorcycle daredevil is attempting to jump across as many buses as possible. The takeoff ramp makes

an angle of 18º above the horizontal, and the landing ramp is identical to the takeoff ramp. The buses are

parked side by side, and each bus is 2.74m wide. The cyclist leaves the ramp with a speed of 33.5m/s. What

is the maximum number of buses over which the cyclist can jump?

Ans)24 buses

http://www.physics.brocku.ca/~edik/dr.fun/roach-ramp-jump.jpeg



2 where vy= vsinθ

𝒗 = √𝒗𝒙𝟐 + 𝒗𝒚

𝟐

5. A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of 8m/s at

an angle of 20˚ below the horizontal. It strikes the ground 3s later. (i) How far horizontally from the base of

the building does the ball strike the ground? ii) How long does it take the ball to reach a point 20m below

the level of the throw? Ans) 22.6m , 1.76s

( If necessary, use quadratic formula : if ax2+bx +c=0, then x = −𝑏±√𝑏2−4𝑎𝑐

2𝑎 )

20°

6. A helicopter is flying horizontally at a speed of 60m/s when it drops a bomb at an elevation of 300m. (a)

How far does it travel horizontally while falling? (b) If the velocity of the helicopter remains constant,

where is the helicopter when the bomb hits the ground? That is, behind, in front or right above the bomb.

Justify your answer~!

Ans) (a) 7.82s (b) right above

7. A stone is thrown from the top of a wall upward at an angle of 30° to the horizontal and with an initial

speed of 20m/s. If the height+arm release point is 4m above the ground, i) find the time(s) when the stone

is 1m above the release point and ii) find the speed of the stone at t = 2.1s and the x and y coordinates at

that time (ax2 + bx + c = 0, x= −𝑏±√𝑏2−4𝑎𝑐

2𝑎 )

4m

Ans) i) 0.105s and 1.94s ii) 20.3m/s, x=36.4m , y= -0.61m

8. A fire hose ejects a stream of water at an angle of 35° above the horizontal. The water leaves the nozzle

with a speed of 25m/s. Assuming that the water behaves like a projectile, how far from a building should

the fire hose be located to hit the highest possible fire

Ans) 29.96m



2 where vy= vsinθ

𝒗 = √𝒗𝒙𝟐 + 𝒗𝒚

𝟐

9. A soccer player kicks the ball toward a goal that is 29m in front of him. The ball leaves his foot at a

speed of 19m/s and an angle of 32° above the horizontal ground. Find the speed of the ball when the goalie

catches it in front of the net. Also find the x, y coordinates when the ball is caught with respect to the where

ball was kicked.

Y

(x,y) = ?

X

origin(0,0)

Ans) 17.8m/s , (29, 2.25)

TEST IIB

Solve the following questions. ( 8points) You must show your work~! Calculator in degrees!! 4. A firefighter 50m away from a burning building directs a stream of water from a fire hose at an angle of

30˚ above the horizontal. If the speed of the stream is 40m/s, at what height will the water strike the

building? Ans) 18.64m

5. The highest barrier that a projectile can clear is 13.5m, when the projectile is launched at an angle of 15°

above the horizontal. What is the projectile’s launch speed?

Ans) 62.85m/s

6. A rocket is fired at a speed of 75m/s from ground level, at an angle of 60° above the horizontal. The

rocket is fired toward an 11m high wall, which is located 27m away. By how much does the rocket clear

the top of the wall?

Ans) 33.2m

8. A horizontal rifle is fired at a bull’s-eye. The muzzle speed of the bullet is 670m/s. The barrel is pointed

directly at the center of the bull’s-eye, but the bullet strikes the target 0.026m below the center. What is the

horizontal distance between the end of the rifle and bull’s-eye?

Ans) 48.8m

9. An Olympic jumper, on his 1st jump, leaves the ground at an angle of 23° and travels through the air for a

horizontal distance of 8.7m before landing. Remembering that he can travel further at a different angle, on

his 2nd jump he leaves the ground at a greater angle. How far will he cover on his 2nd jump? (hint: first find

the initial speed by using x = vx t & vyf = vyi – gt and then use the appropriate angle that gives maximum

horizontal distance)

Ans) 12.2



2 where vy= vsinθ

𝒗 = √𝒗𝒙𝟐 + 𝒗𝒚

𝟐

TEST IIC

Solve the following questions. ( 8points) You must show your work~! Calculator in degrees!!

4. A tennis ball rolls off the edge of a tabletop 0.75m above the floor and strikes the floor at a point 1.4m

horizontally from the edge of the table. (a) Find the time of flight of the ball (b) find the initial speed of the

ball and (c) find the speed of the ball just before it strikes the floor

Ans) 0.39s, 3.6m/s, 5.24m/s

5. A ball shoots upward at an angle of 40° to the horizontal. The initial speed of the ball is 20m/s. (a) How

high up will it strike a wall which is 8m away? (b) What is the speed the moment it strikes the wall? (c) Did

the ball hit the wall on its way down or up? Ans) 5.36m , 17.2m/s, up Wall

vi

8m

6. The acceleration due to gravity on the moon is gmoon=1.62m/s². If you kick a football at an angle of 40°

to the horizontal with an initial speed of 22m/s on the moon, what are the maximum height and the range?

Ans) 61.7m, 295m

7. An artillery shell is fired with an initial speed of 300m/s at 55° above the horizontal. It explodes on a

mountainside 42s after firing. What are the x and y coordinates of the shell where it explodes, relative to its

firing point?

Ans (7227, 1678)

8. The drawing below shows an exaggerated view of a rifle that has been ‘sighted’ for a 91.4m target. If the

muzzle speed of the bullet is vi =427m/s, what is the possible angle θ between the rifle barrel and the

horizontal such that the bullet will hit the target? Ans) 0.14°

(useful information; 2sinθcosθ = sin2θ)

θ=?

91.4m

TEST IIIA ΣF = ma , f = μ FN

1. An object is on a frictionless surface. The mass of the object is 3.5kg. A force gives the object an

acceleration of 2.2m/s2. What is the force?

a) 15.4N b) 11.6N c) 7.7N d) 3.5N

2. If the weight of an object is 87N, find the mass of the object.

a) 13.6kg b) 8.9kg c) 6.2kg d) 1.5kg

3. A Force of 11.8N is applied for 6s to a 2.8kg box initially at rest on a frictionless surface. What is the

speed of the box at the end of the 6s interval? (hint: use vf = vi + at to find the speed)

a) 3.8m/s b) 18.2m/s c) 25.3m/s d) 37.5m/s

4. An 8kg box is released on a 30º inclined plane and slides down a frictionless inclined plane. Find the

acceleration of the box.

a) 4.9m/s2 b) 3.4m/s2 c) 2.2m/s2 d) 1.4m/s2

5. A 4kg box is pulled by a 16.2N force parallel to a rough surface. The coefficient of kinetic friction μk is

0.12. Draw a free-body diagram and find the acceleration of the box. Ans) 2.87m/s2

Fapp

6. A crate of mass 100kg with an initial speed of 7.6m/s is gliding across

the ice. The coefficient of kinetic friction is μk = 0.1. How far will the

crate travel before it comes to a rest? Use vf 2-vi

2=2ad to find the

distance)

Ans) 29.5m

7. The coefficients of static and kinetic friction between a 48.6kg crate and the floor are 0.615 and 0.420,

respectively. A worker gradually increases his horizontal push against this crate until it just begins to move

and from then on maintains that same maximum push. What is the acceleration of the crate after it has

begun to move? Ans) 1.91m/s2

8. Suppose that a 28kg box is pulled by a 100N force at an angle of 25° to the horizontal. The coefficient of

kinetic friction μk is 0.15. Draw a free-body diagram and find the acceleration of the box

Fapp Ans) 2m/s2

θ

ΣF = ma , f = μ FN

9. The coefficient of kinetic friction between block m1 and the table is µk =0.1. Also, m1=6kg, m2=5kg.

A horizontal force of Fapp=110N is pulling on the m1. What is the acceleration of the system?

Ans) 5m/s2

m1

Fapp

m2

10. New cars are equipped with antilock brakes that prevent tires from sliding on slippery roads during

sudden stops. A Honda Accord is traveling at a speed of 17.9m/s on a snow-packed road when the driver

applies the brakes. The effective coefficient of static friction with and without antilock brakes is 0.764 and

0.615, respectively. How much less is the stopping distance with antilock brakes than without antilock

brakes? (*~Use vf 2-vi

2=2ad to find the distance)

Ans) 5.2m

11. A girl is sledding down a slope that is inclined at 30° with respect to the horizontal. A moderate wind is

aiding the motion by providing a steady force of 105N that is parallel to the motion of the sled. The

combined mass of the girl and sled is 65kg, and the coefficient of kinetic friction between the sled and the

snow is 0.15. How much time is required for the sled to travel down a 175m slope, starting from rest? (Use

‘d=vi t + ½at2’ to find the time) Ans) 8.2s

12. At night while it is dark, a driver inadvertently parks his car on a drawbridge. Later the bridge must be

raised to allow a boat to pass through. The coefficient of static friction and kinetic friction between the car's

tire and bridge are µs =0.75 and µk =0.55, respectively. (a) At what angle will the car just start to slide? (b)

If the bridge attendant sees the car suddenly slide and immediately turns off the bridge motor, what will be

the car's acceleration after it has begun to move? (useful info : sinθ/cosθ=tanθ)

Ans) 36.9°, 1.57m/s2

TEST IIIB



a) 11.4N b) 9.9N c) 7.2N d) 3.5N


a) 13.6kg b) 8.9kg c) 5.7kg d) 1.5kg



a) 3.8m/s b) 11.4m/s c) 20.3m/s d) 31.5m/s


4. A m1=10kg mass on a horizontal friction-free air track table is accelerated by a string attached to

another m2=10kg mass hanging vertically from a pulley. What is the acceleration of the system of both

masses?

a) a=4.9m/s2 b) a=2.4m/s2 c) a=1.1m/s2 d) a=0.5m/s2

m1

m2


0.12. Draw a free-body diagram and find the acceleration of the box. Ans) 1.6m/s2

Fapp

6. A stuntman is being pulled along a rough road at a constant speed, by a cable attached to a moving truck.

The cable is parallel to the ground. The mass of the stuntman is 109kg, and the coefficient of kinetic

friction between the road and him is 0.87. Find the tension force of the cable.

Ans) 929N



Fapp

θ Ans) 3.2m/s2



m1

Fapp

Ans) 6.1m/s2

m2


10. A rope holds a block of mass 10kg at rest on a frictionless inclined plane

as shown.

i) Determine the tension in the rope

Ans) 49N

θ=30°

ii) Which of the following statements concerning the force exerted on the plane by the rock(=FN) is true?

Justify the answer you have chosen.

a) It is 0N b) It is 98N c) It is greater than 98N d) It is less than 98N, but greater than 0N

Ans) d)

iii) Determine the acceleration of the rock down the inclined plane if the rope breaks.

Ans) 4.9m/s2

11. A penguin slides at a constant speed of 1.4m/s down an icy incline. The incline slopes above the

horizontal at an angle of 6.9°. At the bottom of the incline, the penguin slides onto a horizontal patch of ice.

The coefficient of kinetic friction between the penguin and the ice is the same for the incline as for the

horizontal patch. How much time is required for the penguin to slide to a halt after entering the horizontal

patch of ice? (Use ‘vf =vi + at’ to find the time. Useful info : sinθ/cosθ=tanθ)

Ans) 1.2s

12. A wooden crate is sliding on a surface of snow with a constant speed. The crate approaches a snowy

hill with an angle of 40° above the horizontal. The coefficient of kinetic friction of the surface of the hill is

μk = 0.30. (a) Find the acceleration of the crate as it is going up the hill. (b) The crate eventually stops and

slides back down. Find the acceleration as it slides down. Ans) -8.55m/s2, 4.05m/s2

40°

TEST IIIC



a) 12.1N b) 9.9N c) 7.2N d) 3.5N


a) 13.6kg b) 8.9kg c) 6.2kg d) 4.5kg



a) 8.7m/s b) 11.4m/s c) 20.3m/s d) 31.5m/s

4. Two forces act on a 4.5kg block resting on a frictionless

surface. What is the horizontal acceleration of the block?

a)1.8m/s2 b) 1.2m/s2 c) 0.82m/s2 d) 3.2m/s2

5.9N

3.7N 43°



0.12. Draw a free-body diagram and find the acceleration of the box.

Fapp

Ans) 3.4m/s2

6. A boy on a sled is being pushed horizontally by his older brother resulting in an acceleration of 2.4m/s2.

The force resisting the motion is 450N. The mass of the bobsled and boy is 270kg. Find the pushing force

exerted by the brother.

Ans) 1098N



Fapp

θ

Ans) 4m/s2



m1

Fapp

Ans) 2.33m/s2

m2

10. A cart of mass m=3kg is initially at rest on a frictionless air track. Two forces, F1 =12N and F2 =12N

simultaneously acts on the cart. After 4 seconds, what is the position of the block? d=½at2

F1

F2

25° 10°

Ans) -2.51m

-3.0m -2.0m -1.0m 0.0m 1.0m 2.0m 3.0m

11. A crate is sliding down a ramp at constant speed. The mass of the crate is 80kg, and the ramp is inclined

at 15° with respect to the horizontal. Frictional force between the crate and ramp is what results in constant

speed of the crate. If the crate now is pushed up the same ramp, how much pushing force is needed to go up

the ramp at constant speed?

Ans) 406N


12. 8kg box is released from rest on a 30° inclined rough plane and accelerates down the incline. The

coefficient of friction of the incline plane is µk =0.54. The distance from the block and the end of the ramp

is 4m. The block will eventually slide off the ramp and continue on a frictionless surface. If the box

approaches another ramp of inclined angle of 40°, how far up will the box reach if the ramp is also

frictionless? (use vf 2-vi

2=2ad to find 'v' or ‘d’) Ans) 0.2m

Circular Motion f =µFN ∑ Fr = 𝑚𝑣2

𝑟

1. If a car goes through a curve too fast, the car tends to slide out of the curve. Especially when the road is

wet or icy, the friction between the tires and road cannot be reliable. To prevent this, highways are banked

when the roads are curved. If a car is expected to move around a curve of radius 200m at 25m/s, what

should be the value of the banking angle if no dependence is to be placed on friction? Also draw a free-

body diagram to represent the forces.

Fr

ans) 17.7°

2.A small ball is fastened to a string L=0.24m long and suspended from a

fixed point P to make a conical pendulum. The ball describes a horizontal

circle about a center and the string makes an angle of 15° with the vertical.

Find the speed of the ball and also draw a free-body diagram to represent the

forces.

ans) 0.404m/s

θ

3. At an amusement park there is a ride in which cylindrical shaped

chambers spin around a central axis. People are standing on the floor facing

the axis, their backs against the wall. When the chamber reaches the speed

of 3.2m/s, the floor opens but the people stay on the wall. An 83kg person

feels a 560N force pressing against his back.

i) Draw a free-body diagram to represent the forces.

ii) What is the radius of a chamber?

Ans) 1.5m

iii) What is the coefficient of friction?

Ans) 1.45

midterm exam review(physicsi)...midterm exam review(physicsi) testii true or false 1. the length of...

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