Two particles are located in an xy coordinate system. Particle 1 (mass m1 = 10.0 kg) is fixed at the origin. Particle 2 (mass m2 = 20.0 kg) is initially located on the x axis (θ = 0) at distance r = 2.00 m from the origin and particle 1. This situation is depicted in the simulation (linked below). Simulation The Gravitational Force Question 1 For the given position of the two particles, express the gravitational force on particle 1 due to particle 2, F→12, in unit-vector notation. Glive your answer in nanonewtons, and fill in the boxes below. F→12 = (nN)i^+(nN)j^ Click if you would like to Show Work for this question: Open Show Worik Attempts: 0 of 8 used SAVE FOR LATER SUBMIT ANSWER Question 2 For the default position of particle 2, express the gravitational force on particle 2 due to particle 1, F→21, in unit-vector notation. Give your answer in nanonewitons, and fill in the boxes below. F→21 = (nN)i^+(nN)j^ Question 4 What value for the angle θ in the range 0 ≤ θ ≤ 90∘ results in the following gravitational force on particle 1:F→12 = (22.0 nN)i^+(8.88 nN)j^? θ = the tolerance is +/−2% Click if you would like to Show Work for this question: Open Show Work Question 5 What value for the distance r between the two particles results in the following gravitational force on particle 1: F→12 = (22.0 nN)i^+(8.88 nN)j^? r = m the tolerance is +/−2%
A block of mass M = 5.10 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6190 N/m. A bullet of mass m = 8.20 g and velocity v→ of magnitude 620 m/s strikes and is embedded in the block (see the figure below). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion. (a) Number Units (b) Number Units
A 320 kg rocket sled can be accelerated at a constant rate from rest to 1000 km/h in 2.6 s. What is the magnitude of the required net force? Number Units
The current entering an element between 0 and 5 ms is shown below. What is the total charges entering this element in μC? 9 −9 8.5 7.5
The two vectors a→ and b→ in the figure have equal magnitudes of 11.7 m and the angles are θ1 = 34∘ and θ2 = 106∘. Find (a) the x component and (b) the y component of their vector sum r→, (c) the magnitude of r→, and (d) the angle r→ makes with the positive direction of the x axis. (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The two vectors a→ and b→ in the figure have equal magnitudes of 11.2 m and the angles are θ1 = 34∘ and θ2 = 103∘. Find (a) the x component and (b) the y component of their vector sum r→, (c) the magnitude of r→, and (d) the angle r→ makes with the positive direction of the x axis.
Sunjamming. A "sun yacht" is a spacecraft with a large sail that is pushed by sunlight. Although such a push is tiny in everyday circumstances, it can be large enough to send the spacecraft outward from the Sun on a cost-free but slow trip. Suppose that the spacecraft has a mass of 801 kg and receives a push of 19.0 N. (a) What is the magnitude of the resulting acceleration? If the craft starts from rest, (b) how far will it travel in 1 day and (c) how fast will it then be moving? (a) Number Units (b) Number Units (c) Number Units
A bowling ball (mass = 5.9 kg, radius = 0.11 m) and a billiard ball (mass = 0.38 kg, radius = 0.028 m) may each be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other? Number Units
Two identical point charges (+2.39×10−9 C) are fixed in place, separated by 0.600 m (see the figure). Find (a) the electric field and (b) the electric potential at the midpoint of the line between the charges qA and qB. (a) Number Units (b) Number Units
A particle possessing q = 7.25 μC of charge and a mass of m = 6.55 g is fired at a speed of v = 255 cm/s between two horizontal charged plates of length L = 44.7 cm. Assume that the electric field between the plates is uniform and has a constant value of E = 1770 N/C, directed upwards. Calculate the distance y by which the charge falls below a straight-line path when it reaches the end of the plates. Assume a gravitational acceleration of g = 9.81 m/s2. What field strength will allow the particle to pass between the plates along a straight path? field strength: N/C
A planet of mass 7×1024 kg is at location < −8×1011, 5×1011, 0 > m. A star of mass 6×1030 kg is at location < 9×1011, −7×1011, 0 > m. What is the force exerted on the planet by the star? (It will probably be helpful to draw a diagram, including the relevant vectors.) F→onplanet = <, > N
What are the magnitude and direction of the force exerted on a 3.72 μC charge by a 270 N/C electric field that points due east? magnitude N direction
To study the properties of various particles, you can accelerate the particles with electric fields. A positron is a particle with the same mass as an electron but the opposite charge (+e). If a positron is accelerated by a constant electric field of magnitude 312 N/C, find the following. (a) Find the acceleration of the positron. m/s2 (b) Find the positron's speed after 7.55×10−9 s. Assume that the positron started from rest. m/s
At a particular instant the magnitude of the gravitational force exerted by a planet on one of its moons is 8×1021 N. Part 1 (a) If the mass of the moon were 9 times as large, what would the magnitude of the force be? |F→| = N Part 2 (b) If instead the distance between the moon and the planet were 9 times as large (no change in mass), what would the magnitude of the force be? |F→| = N
An electron and a proton, starting from rest, are accelerated through an electsic potential difference of the same magnitude. In the process, the electron acquires a speed ve, while the proton acquires a speed vp. Find the ratio ve/vp. ve/vp = Number Units
28 The diagram shows a tuning fork above a tube of air of length 25 cm. A stationary wave is set up in the tube with the same frequency as the tuning fork. The lower end of the tube is sealed. This is the minimum length of tube with the lower end sealed that creates a stationary wave. Which other lengths of tubes, sealed at their lower end, will also create a stationary wave? A 37.5 cm and 50 cm B 50 cm and 75 cm C 75 cm and 100 cm D 75 cm and 125 cm
A cube with side length of 2 m is oriented with its edges (ae, ab, and ad) aligned with the x, y, and z axes. A uniform electric field E of 200 N/C lies in the xz-plane, making a θ = 60∘ angle with the positive x-axis. Calculate the electric flux through the face efgh of the cube. Express your answer in units of N⋅m2/C.
The figure below shows a section of a very thin, very long, straight rod with a uniform charge per unit length of λ. Point O is a perpendicular distance d from the rod. A spherical gaussian surface is centered at point O and has a radius R. (Use any variable or symbol stated above along with the following as necessary: ε0.) (a) What is the electric flux through the spherical surface if R < d? ΦE = (b) What is the electric flux through the spherical surface if R > d? ΦE =
Swimmers at a water park have a choice of two frictionless water slides as shown in the figure. Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2? (A) v1 > v2 (B) v1 < v2 (C) v1 = v2 (D) No simple relationship exists between v1 and v2 because we do not know the curvature of slide 2.
An ac generator with Em = 229 V and operating at 392 Hz causes oscillations in a series RLC circuit having R = 226 Ω, L = 145 mH, and C = 23.8 μF. Find (a) the capacitive reactance XC, (b) the impedance Z, and (c) the current amplitude I. A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d) XC, (e) Z, and (f) I increase, decrease, or remain the same. (a) Number Units (b) Number Units (c) Number (d) (e) (f)
A seated musician plays a G5 note at 784 Hz. How much time Δt does it take for 121 air pressure maxima to pass a stationary listener? Δt = s You would like to express the air pressure oscillations at a point in space in the given form. P(t) = Pmaxcos(Bt) If t is measured in seconds, what value should the quantity B have? What units should it have? B = Units of B:
For a damped oscillator with a mass of 340 g, a spring constant 83 N/m and a damping coefficient of 79 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 20 cycles? Number Units
An electric dipole consists of charges +2e and −2e separated by 0.86 nm. It is in an electric field of strength 4.3× 106 N/C. Calculate the magnitude of the torque on the dipole when the dipole moment is (a) parallel to, (b) perpendicular to, and (c) antiparallel to the electric field. (a) Number Units (b) Number Units (c) Number Units
A seated musician plays an A#5 note at 932 Hz. How long does it take for 721 air pressure maxima to pass a stationary listener? time to pass: s You would like to express the air pressure oscillations at a point in space in the given form. P(t) = Pmaxcos(Bt) If t is measured in seconds, what value should the quantity B have? B = If t is measured in seconds, what units should the quantity B have?
Two electromagnetic waves are emitted from a source. Wave A has a wavelength of 329 nm while Wave B has a wavelength of 645 nm. a) What is the speed of Wave A? v = m/s b) What is the frequency of Wave A? fA = Hz c) What is the speed of Wave B? v = m/s d) What is the frequency of Wave B? fB = Hz