(2nd variant, 7kg is 3 times faster than 21kg)
The working equation for this is: E = F/Q, where E is the strength of electric field, F is the force and Q is the charge. The force is equal to:
F = mg = (0.13/1000 kg)(9.81 m/s²) = 1.2753×10⁻³ N
The charge of he excess electrons is equal to:
Q = (-1.6021766208×10⁻¹⁹ C/electron)(1×10¹⁰ electrons)
Q = -1.6021766208×10⁻⁹ C
E = 1.2753×10⁻³ N/-1.6021766208×10⁻⁹ C
E = -795,979.66 N/C
Answer:
A. False
B. False
C. True
D. True
E. True
F. True
Explanation:
A. The equation Ax=b is referred to as a matrix equation and not vector equation.
B. If the augmented matrix [ A b ] has a pivot position in every row then equation Ax=b may or may not be consistent. It is inconsistent if [A b] has a pivot in the last column b and it is consistent if the matrix A has a pivot in every row.
C. In the product of Ax also called the dot product the first entry is a sum of products. For example the the product of Ax where A has [a11 a12 a13] in the first entry of each column and the corresponding entries in x are [x1 x2 x3] then the first entry in the product is the sum of products i.e. a11x1 + a12x2 +a13x3
D. If the columns of mxn matrix A span R^m, this states that every possible vector b in R^m is a linear combination of the columns which makes the equation consistent. So the equation Ax=b has at least one solution for each b in R^m.
E. It is stated that a vector equation x1a1 + x2a2 + x3a3 + ... + xnan = b has the same solution set as that of the linear system with augmented matrix [a1 a2 ... an b]. So the solution set of linear system whose augmented matrix is [a1 a2 a3 b] is the same as solution set of Ax=b if A=[a1 a2 a3] and b can be produced by linear combination of a1 a2 a3 iff the solution of linear system corresponding to [a1 a2 a3 b] takes place.
F. It is true because lets say b is a vector in R^m which is not in the span of the columns. b cannot be obtained for some x which belongs to R^m as b = Ax. So Ax=b is inconsistent for some b in R^m and has no solution.
W = F x d/x = (m x Ag) x h, therefore, mass (2kg x 9.8) x 2.5m = 49J
