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21 Terms

1
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A circular metal plate has a radius of 50 cm, a thickness of 20 cm, and a mass of 425 kg. Density of the metal is: [ Note: Area of a circle is πr2]

Find your volume first, use V = πr2h

Then, find Density with: D = m/v

(2700 kg)

2
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Three displacement vectors are in an x-y plane as shown in the following figure.

(a) express these vectors in unit vector notation.

(b) Find the resultant vector R if R = A + B + C

A = 5 m, B = 10 m, C = 15m; B & C at 30o

Find the x- and y- components of the vectors A, B, C with Axcosθ, Aysinθ, Bcosθ, etc…

Line them up, and add the i and j components to find the resultant vector R

3
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Two vectors are given by vector A = 3i + 4j + 5k and vector B = 2i - 6j + 7k.

a) Find A . B

b) What is the angle between the vectors

(a) Multiply the vectors A and B together to get A . B

(b) Find the magnitudes of vectors A and B. Then, use A . B/AB. Multiply the answer by the inverse of cos.

4
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A projectile is fired at an angle of 30o above the horizontal level ground with a speed of 10 m/s. Its speed at maximum height is…?

Find the x- component, since the projectile flies at a horizontal level. x = vcosθ

8.66 m/s

5
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An object rotating along a horizontal circular path of radius 2 m at a constant rate of 40 rpm. What is its speed and acceleration?

Convert rpm to rad/s. (1 rev = 2π rad)

Find linear speed: v = ωr

Then, find centripetal acceleration: ar=(v2/r)

(its speed is 8.37 m/s and the acceleration is 35.1 m/s2)

6
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If the only forces working on a mass of 5-kg are F1 = (3i -8j)N and F2 = (5i + 3j)N, the magnitude of acceleration of the mass is…?

Find Fnet by adding the forces together. Then, find the magnitude of the solution

Find acceleration with: a = Fnet/ m

1.89 m/s2

7
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A stone is thrown horizontally from the edge of a building with a speed of 20m/s. It strikes the level ground at a distance of 50 m from the base of the building. [Neglecting air resistance]

(a) What is the height of the building?

(b) How long will the stone be in the air?

Find time (t) seconds with the velocity formula: v = d(t).

Find height with the free fall equation: Δy = voyt - ½ (g) (t)2

t = 2.5s

H = 30.625

8
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A particle starts from the origin with a velocity of vector v = 3i + 5j and a constant acceleration of vector a = 2i -3j, where v is in m/s and a is in m/s2.

(a) What is the particle’s distance from the origin after 5 seconds?

(b) What is its speed after 10 seconds?

Δr = vot + ½ at2 to find the displacement. Then, use the magnitude formula

v = vo + at to find the speed. Use magnitude formula

9
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A block of mass m = 25 kg is pulled along a horizontal frictionless floor with an acceleration of 0.4 m/s2 by applying a force F at an angle θ = 35o.

(a) Draw the for diagram (free body diagram) of the block

(b) Find the magnitude of F, and

(c) Find the normal force

Apply newton’s law formula (ma/cosθ) with the given acceleration and mass to find the force F.

Find N with mg - Fsinθ

10
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A box is sliding down slope along an incline with an angle of inclination of 20o with the horizontal

(a) Draw the force diagram of the box and find

(b) the acceleration of the box.

Use the formula for acceleration down a slope: a = gsinθ

11
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Two ice-skaters A (mass 60 kg) and B (mass 80 kg) are standing on an ice floor next to each other and talking. Suddenly A pushed B. As a result, B moves to the right with a speed of 3 m/s. What happens to A?

Use Pbefore = Pafter: m1v1 + m2v2 = m/s

(-4m/s)

12
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A 0.5 kg steel ball is thrown horizontally at 10 m/s. The ball hits a wall and
rebounds at 10 m/s. The ball was in contact with the wall for 2 ms. Find
(a) Initial and final linear momentum
(b) Change in linear momentum
(c) Average force exerted on the
wall by the ball (or on the ball by wall)
(d) Compare this force with the
gravitational force on the ball (weight)

(a) Find the final and initial momentum: pi = mvi/ pf = mvf

(b) Change in momentum: ΔP = Pf - Pi

(c) Find average force: Favg=(ΔP/Δt)

13
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Planet A orbits around a star Z with a period of 4.7x107 s. Using the following
data, find
(a) gravitational force between Planet A and Star Z,
(b) magnitude of acceleration due to gravity on the surface of Planet A,
(c) gravitational potential energy of Planet A and Star Z system,
(d) escape speed from Planet A, and
(e) total energy of Planet A.

[G = 6.67 × 10-11 N.m2/kg2]

Planet A

Mass = 7.98 X 1024 kg

Radius = 6.85 x 106 m

Star Z
Mass = 2.4 x 1030 kg
Radius = 7.75 x 108 m

(a) Find r with Kepler’s third law: r = take the cubed root of T2GM/4π2. Use it to find F with Gmamz/r2

(b) Use g = GM/R2

(c ) UAZ= -Gmamz/r

(d) square root of 2GM/R

(e) -Gmamz/2r

14
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A 1.2-kg object moving with a speed of 8.0 m/s collides perpendicularly with a wall and emerges with a speed of 6.0 m/s in the opposite direction. If the object is in contact with the wall for 2.0 ms, what is the magnitude of the average force on the object by the wall?

Calculate the change in momentum: mvf - mvi

Solve for the average force: Favg = |ΔP|/Δt

(8.4 kN)

15
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A 3.0-kg ball with an initial velocity of (4i + 3j) m/s collides with a wall and rebounds with a velocity of (-4i + 3j) m/s. What is the impulse exerted on the ball by the wall?

Δp = m(vf - vi)

(-24i N s)

16
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A 10-g bullet moving 1000 m/s strikes and passes through a 2.0-kg block initially at rest, as shown. The bullet emerges from the block with a speed of 400 m/s. To what maximum height will the block rise above its initial position?

Find the velocity of the block: mbvbi = mbvbf + mblockvblock

Find the height: h = v2block/2g

(46 cm)

17
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A 2.0-kg object moving 5.0 m/s collides with and sticks to an 8.0-kg object initially at rest. Determine the kinetic energy lost by the system as a result of this collision.

Find the total momentum: m1v1 + m2v2. Then the combined mass, m1 + m2

Divide the solutions for the vf.

KEinitial = ½ m1v12 + ½ m2v22

KEfinal = ½ (pf)(mf)

Subtract KEi- KEf

(20 J)

18
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A pendulum consists of a 1.6-kg block hanging on a 2.0-m length string. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 10-g bullet moving horizontally in the opposite direction. The bullet remains in the block and causes the block to come to rest at the low point of its swing. What is the magnitude of the bullet’s velocity just before hitting the block?

Find v with: square root 2gh.

-m/mb (vblock)

(1.0 km/s)

19
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The period of a satellite circling planet Nutron is observed to be 84 s when it is in a circular orbit with a radius of 8.0 X 106 m. What is the mass of planet Nutron?

Find the mass with: M = 4π2r3/GM

(4.3 X 1028 kg)

20
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What is the escape speed from a planet of mass M and radius R if M = 3.2 X 1023 kg and R = 2.4 X 106 m?

Use the escape velocity formula: vesc = square Root (2GM/R)

divide by 1000

(4.2 km/s)

21
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