In an inertial frame of reference, a series of experiments is conducted. In each experiment, two or three forces are applied to an object. The magnitudes of these forces are given. No other forces are acting on the object. In which cases may the object possibly move at a constant velocity of 256m/s?

(1) 2 N; 2 N
(2) 200 N; 200 N
(3) 200 N; 201 N
(4) 2 N; 2 N; 4 N
(5) 2 N; 2 N; 2 N
(6) 2 N; 2 N; 3 N
(7) 2 N; 2 N; 5 N
(8) 200 N; 200 N; 5 N

(1) 2 N; 2 N

(2) 200 N; 200 N

(4) 2 N; 2 N; 4 N

Explanation:

For the body to move with a constant velocity the acceleration must be zero. Because, acceleration is the rate of change of velocity. And for zero acceleration, the net unbalanced force must also be equal to zero. According to Newton's Second Law:

F = ma = m(0) = 0

Therefore, object can move with constant velocity of 256 m/s, in those cases, for which the vector sum of the forces can somehow become zero.

Those cases are mentioned below, with the expression for zero net force:

(1) 2 N; 2 N : F = 2 N - 2 N = 0 N

(2) 200 N; 200 N : F = 200 N - 200 N = 0 N

(4) 2 N; 2 N; 4 N : F = 2 N + 2 N - 4 N = 0 N (OR) F = 4 N - 2 N - 2 N = 0 N

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft