Kinetic energy KE has dimensions kg · m2/s2. It can be written in terms of the momentum p and mass m as(a) Determine the proper units for momentum using dimensional analysis. (b) Refer to Problem 1. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p.Problem 1: Newton’s law of universal gravitation is represented byWhere F is the gravitational force, M and m are masses, and r is a length. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G?

A) Given the vectors A⃗ A→ and B⃗ B→ shown in the figure ((Figure 1)), determine the magnitude of B⃗ −A⃗ B→−A→. B) Determine the direction of B⃗ −A⃗ C) Determine A⃗ −B⃗ A→−B→ without using your answer in parts AA and BB. Then compare your results and see if they are opposite. Determine the magnitude of A⃗ −B⃗ A→−B→. D) Determine the direction of A⃗ −B⃗ A→−B→.

The weight of one dozen apples is 4.3 lb. Determine the average mass of one apple in both SI and US units and the average weight of one apple in SI units. In the present case, how applicable is the "rule of thumb" that an average apple weighs 1 N? Answers: Mass of one apple = Mass of one apple = Weight of one apple = i i i kg slugs N

Let A⃗ =(9,78∘) and B⃗ =(2,289∘), where the angles are measured counterclockwise from the positive x-axis. What is C⃗ =4A⃗ +B⃗ ? Give your answer in component form. x component: y component:

The Statue of Liberty in New York City is approximately 305 ft305 ft tall. How many U.S. dimes would be in a stack of the same height? Each dime is 1.35 mm1.35 mm thick. number of dimes:     Each dime has a mass of 2.268 g.2.268 g. How much would the stack of dimes from the previous question weigh? mass:   g What is the value, in dollars, of the same stack of dimes? value:   dollars The 2017 U.S. gross domestic product (GDP) was valued at 19,390,604,000 dollars.19,390,604,000 dollars. How many Statue of Liberty‑height stacks of dimes are needed to match the GDP in value? number of stacks:

In the equation of motion, F = ma, a indicates A. Acceleration of largest particle B. Acceleration of the center of mass of the system C. Gravitational force D. None of the above

1. In this problem, you will work out the dimensions and units of quantities from equations. This is a very useful method for checking the physical validity of equations. (a) Consider a particle whose position x is given as a function of its speed v by the following equation v = Ce¯x, where b and C are positive constants. Find the units of C and b in the S.I system. Practice Quiz1 (b) Consider a particle velocity v is given as a function of time t by the following equation, v= Aw sin(at) where A, o are positive constants. Find the units of A and in S.I units. 2. A particle is moving in a straight line. The graph denotes the velocity of the particle as a function of time. (a) Draw a graph of the acceleration of the particle as a function of time. Your graph should include the magnitude and sign of the acceleration. (b) Draw a graph of the displacement of the particle as a function of time. The particle starts from x = 0. 10 8 (s/w) A AA 2.6 -8 -10- t (sec)