4. A 1.5 kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0m?
5. If the vectors A and B have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is -100, what is the magnitude of the sum of these two vectors?
6. Two vectors A and B are given by A = 4i + 8j and B = 6i - 2j. The scalar product of A and third vector C is -16. The scalar product of B and C is +18. The z component of C is 0. What is the magnitude of C?
Let's first compute how much work the force performs on the object as it moves from x = 0 meters to x = 3 meters. This is given by the integral of F dx. From x = 0 meters to 2 meters F is positive and the contribution to the integral is the area enclosed by the x-axis, the y-axis and the graph of the force which is 8 J.
From x = 2 meters to 3 meters the contribution to the integral is minus the area anclosed by the graph, the segment on the x-axis from x = 2 meters to x = 3 meters and the line parallel to the y axis given by x = 3 meters. This contribution is thus minus 2 J.
So, the total gain in kinetic energy equals 8 J - 2 J = 6 J. The kinetic energy at x = 0 meters was
1/2 * 1.5 kg (4.0 m/s)^2 = 12 J
So, it follows that the kinetic energy at x = 3 meters is 12 J + 6 J = 18 J which is answer a)
Problem ...
Solution Summary
The following post helps with problems involving kinetic energy, magnitude and vectors.
... 4) Define a nontrivial subspace of (show all work). 1) Definition: A vector space is a set of ... satisfying the following properties: Let be vectors in , and let ...
Math: Vector Geometry, Cross Products, and Real Inner Products. ... u and v are given non-zero vectors in the ... u,v} is a linearly independent subset of V. Show work. ...
Vector Geometry, Cross Products and Real Inner Products. ... 1. Write the vector equation of the line in R^3 which ... points P: (1,-1,3) and Q: (2,-1,-1). Show work. ...
...vector orthogonal to the plane of (subspace spanned by) the vectors u and v. Show work. ... That vector is actually a vector which is orthogonal to both u and v ...
... direction parallel to the displacement.It is visible mathematically from the vector form of the work ⃗ formula which is a dot product of force vector ⃗ and ...
...Work is defined by: (1.1) Where F is the force and s is the total displacement vector. Since this is a dot product we can write: (1.2) Where is the angle ...
... Find 2u, -3v, u + v, and 3u - 4v for the given vectors u and v. Show work. 18. ... Show work. ... The solutions consist of details of all kinds of vector operations. ...
... Show your work. ... Thanks for using BrainMass. Vector and Matrix Operations, Row Vectors, Column Vectors, Dot Product and Echelon Form are investigated. ...
... full (as you can see from the earlier working) This gives ... w = r4 into G w' = 0 and test whether each works. ... When you substitute w = r1, and work out G w' = G r1 ...
... Complex 3-space C^3 be equipped with the standard inner product and let ... and u_2= (1/3, 1/3, -1/3). Project the vector v= (1, i, i) onto W. Show work. ...
