PHY131 Ch 1 to 6 Exam Name

A ball is thrown toward a wall at speed 20.0 m/s and at 30.0˚ angle above the horizontal. The wall is distance d = 25.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its velocity as it hits the wall? /
v = dx / dt
vx = 20*cos30
vx = 17.3 m/s 2/2
(b) vx is constant / x = ½ a t2 + vox t + xo
25 = + 20 cos30 t
t = 1.44 sec 6/6 / y = ½ a t2 + voy t + yo
y = -5 t2 + sin30*20 t
y = -10.4 + 14.4
(a) y = 4 m 8/8 / (c) vy = dy / dt
vy = a t + 20 sin30
vy = -10(1.44) + 20 sin30
vy = -4.4 m/s 17/17
Three ballot boxes are connected by cords, two of which wrap over massless frictionless pulleys on opposite ends of the table. The masses are mA = 30 kg, mB = 40 kg, and mC = 20 kg. The frictional coefficient between the boxes and the table is 0.2. When the assembly is released from rest, (a) what is the tension in the cord hanging over the right pulley, and (b) how far does A move in the first 0.300 s (assuming it does not reach the pulley)? The ramp is at an 30 degree angle. / FNet = mt a
6/6 6/6 3/3 4/4
20g – sin30(30g) – Ff = (30+40+20) a
5/5 5/5
50 – (µ(cos30)30g + µ 40g) = 90 a
50 – 0.2 (.866*300 + 400) = 90 a
50 – 132 = 90 a
a = 0 m/s2
FT = m (g – a)
FT = 200 N
/ (b) y = ½ a t2
y = 0 (.3)2
y = 0 m
2/2
A sling-thrower puts a stone (0.250 kg) in the sling's pouch (0.0300 kg) and then begins to make the stone and pouch move in a vertical circle of radius 1.00 m. The cord between the pouch and the person's hand has negligible mass and will break when the tension in the cord is 50.0 N or more. Suppose the sling-thrower could gradually increase the speed of the stone. (a) Will the breaking occur at the lowest point of the circle or at the highest point? (b) At what speed of the stone will that breaking occur? / (a) lowest; (mg opposes the tension which provides the centripetal force) 1/1
/ 6/6 12/12 6/6 2/2 8/8
FT - m g = m v2 / r
50 - .28(10) = .28 v2 / 1
v = 13.0 m/s

The velocity of a particle moving in the xy plane is given by v = (6t - 5t2)i + 9.0j - 10k. At t = 5.0 s and in unit-vector notation, what are (a) the x component and (b) the y component of the acceleration? (c) When (if ever) is the acceleration zero? (d) At what positive time does the speed equal 10 m/s?

(a) ax = dvy / dt
ax = 6 – 10t
ax = 6 – 10(5)
a = (-44 i) m/s2 6/6 / (b)
ay = (0 j) m/s2
6/6 / (c) 0 = 6 – 10t
t = 0.6 sec
10/10 / (d) 12/12
102 = (6t - 5t2)2 + 92 + -102
A 5 kg block is pushed up a ramp by a constant horizontal force of 50 N that is applied by a woman pushing the block. The acceleration of the block is 0.1 m/s2 with a coefficient of friction of 0.20. What is the value of θ? /

Fll = 50 cosθ 2/2
F↓ = 50 sinθ 2/2 / / Fll = 5g sinθ 2/2
F↓ = 5g cosθ 2/2 / FNet = mT (a)
50 (cosθ - sinθ - Ff = mT (a)
50 (cosθ – sinθ)- μ FN = mT (a)
4/4 8/8 4/4 8/8 1/1
50 (cosθ – sinθ)- μ (50(cosθ + sinθ)) = 5(.1)
cosθ – sinθ - 0.2 (cosθ + sinθ) = 0.01
θ = 33.3°
Fll = 50 cosθ - 5g sinθ F↓ = 5g cosθ + 50 sinθ
Fll = 50 (cosθ – sinθ) F↓ = 50(cosθ + sinθ)
Consider a conical pendulum with an 80 kg bob on a 10 m wire making an angle of 30° with the vertical. Determine (a) the radial acceleration of bob. (b) the tangential velocity / 4/4 Ty = mg
cosθ = Ty / T
cosθ = mg / T
T = mg / cosθ
6/6
6/6
sin θ = Tx / T
Tx = T sin θ
Tx = sinθ mg/cosθ
Tx = tanθ mg / (a) 6/6
Fc = Tx
mar = tanθ mg
ar = tanθ g 3/3
ar = 5.77 m/s2
(b) 5/5
mv2/r = tanθ mg
v = (tanθ r g)½ 3/3
v = 5.37 m/s /