Lab #2

Newton's law of universal gravitation is represented by Mm F = G• where F is the gravitational force, M and m are masses, and r is a length. Force has the Sl units kg - m/s?. What are the Sl units of the proportionality constant G?

For the following compartment model, what is the numerical value of the derivative (in Bq/hr) at t=0, 10, and 100 hours if q(0) = 100 Bq and k = 0.02/hr? Be mathematically precise here. Q--k->

Problem 10:  You are a scientist exploring a mysterious planet. You have performed measurements and know the following things: •The planet has radius d.•It is orbiting his star in a circular orbit of radius b.•It takes time T to complete one orbit around the star.•The free-fall acceleration on the surface of the planet is a.  a)Derive an expression for the mass MS of the star in terms of b, T, and G the universal gravitational constant.

QUESTION 3 - The following equation refers to v-pendulum experiment: T4 = (44 L ki g²)(8 m4L/g² )d, where : L: length of the string (2 meters). T: pendulum periodic time d: distance between rods k: pendulum constant g: gravitational acceleration Given that the slope of the graph (T4,d) = -14.2 s4/m, and y-intercept = 13.5 s4, Find the value for g: 9.81 m/s2 O Can't be defined a- 8.51 m/s2 a 10.5 m/s²

Problem A solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. a) Find the tension in the wire. Solution a) 1.

C. Newton's law of universal gravitation states that two particles exert a pull on each other with magnitude F, ([kg - m/s]) that is proportional to the product of their masses mi ([kg]) and m: ([kg]) and inversely proportional to the square of their separation d ([m]). Write down an equation for Newton's law of universal gravitation and determine the Sl unit of all the proportionality constants you used.

Susie's experiment to measure the value of g in Northridge produces a result of 8.90 m/s². The accepted value of g in Northridge is 9.80 m/s². Calculate the percent error in Susie's experiment.

In Newton's 2nd law experiment, the relation between the added mass (M₁) and the inverse of the acceleration M. (kg) (1/a) is shown in the figure. The driving force is constant (M₁0.08 kg). Q5: The magnitude of the gravitational acceleration (in m/s) estimated Slope= 0.85 N from the graph is: a) 11.88 b) 9.50 c) 8.50 d) 13.25 e) 10.63 0.4 1/a (s/m) 06: The mass of the cart Mc (in kg) is: a) 0.30 b) 0.28 c) 0.24 d) 0.20 e) 0.26 M. Mc Mh

A differential equation describing the velocity v of a mass m in fall subject to an air resistance proportional to the instantaneous speed is m dv/dt=mg-kv, where k is a positive proportionality constant. a) Solve the equation, subject to the initial condition v(0) = v0 b) Calculate the limiting speed of the mass. c) If the distance s is related to the speed by ds/dt = v, derive an equationexplicit for s, if it is also known that s(0) = s0 topic:ORDINARY DIFFERENTIAL EQUATIONS

a. During one trial of his experiment, Cavendish measured the force of attraction betweena 158 kg sphere and a 0.730 kg sphere placed 230 mm apart to be 1.74 x 10-7 N.Calculate the universal gravitational constant based on these values. b. Describe two potential sources of error in his measurement.

TIA

The center of a moon of mass m = 8 × 1023 kg is a distance D = 97 × 105 km from the center of a planet of mass M = 10.9 × 1025 kg. At some distance x from the center of the planet, along a line connecting the centers of planet and moon, the net force on an object will be zero.   a. Derive an expression for x.  b.  Calculate x in kilometers, given the variables in the beginning of the problem.

Consider Kepler's equation regarding planetary orbits, given as M = E e sin(E), π where M is the mean anomaly, E is the eccentric anomaly, and e measures eccentricity. Find the eccentric anomaly E when 7 and the eccentricity of the orbit e = 0.37. Use Newton's method with initial approximation Xo = 2 to find x2, rounded to the nearest thousandth. the mean anomaly M = Provide your answer below: Xx₂≈

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Help me to solve this problem step by step and give answer as a 3 significant figures

Can you answer G Mass of the egg is 575

In this problem we are going to compare the strength of the gravitational interaction between the Moon and the Earth and the Sun and the Earth. We will do this by finding the gravitational field g due to the Moon or the Sun, which is the acceleration that the Earth would have if it were interacting with each of them. a) Calculate the magnitude of the gravitational field of the moon at the location of Earth, in meters per square second. b)Calculate the magnitude of the gravitational field of the Sun at the location of Earth, in meters per square second. c)Calculate the ratio of the gravitational field of the Sun to the gravitational field of the Moon, at the location of Earth.

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9. Consider the falling object of mass 10 kg in Example 2, but assume now that the drag force is proportional to the square of the velocity. a. If the limiting velocity is 49 m/s (the same as in Example 2), show that the equation of motion can be written as 1 (49² - 1²). 245 dy dt Also see Problem 21 of Section 1.1. b. If y(0) = 0, find an expression for v(t) at any time. Gc. Plot your solution from part b and the solution (26) from Example 2 on the same axes. d. Based on your plots in part c, compare the effect of a quadratic drag force with that of a linear drag force. e. Find the distance x(t) that the object falls in time t. Nf. Find the time T it takes the object to fall 300 m.

B)how long would it take for a ball dropped from a height of 15.0 meters to land on the surface of this planet? Answer in seconds. Use kinematic equation

At what altitude above Earth's surface would the gravitational acceleration be 1.50 m/s²? (Take the Earth's radius as 6370 km.) Number i Units