M. Ardebil university Physics Test 3 Spring 18 The three forces ahown act on a p

Question

M. Ardebil university Physics Test 3 Spring 18 The three forces ahown act on a particle. Use this exhibit so answer the following questions) 1) Refer to Exhibit. What is the magnitude of the resultant of these three forces? A) 27.0 N D) 23.8N E) 105 N B) 33.2 N C) 36.3 N 2) Refer to Exhibit 3-1. What is the direction of the resaltant of these three forces? A) 35 B) 45 C) 65* D) 53° s E) 85"5 3) The vectors A, B, and are shown. Which diagram below correctly represents resultant of A, B, and Cr b. d. 4) A bullet is fired through a board, 14.0 cm thick, with its line of motion perpendicular to the face of the board. If it enters with a speed of 387 m's and emerges with a speed of 220 m/s, what is the bullet's acceleration as it passes through the board? A)-275 km/s B)-360 km/s C)-500 km/s D)-550 km/s 5) A particle starts from the origin at -0 with a velocity of (16i- 12j) m/s and moves in the xy plane with a constant acceleration of a (3.0i-6.0j) m/s. What is the speed of the particle at r 2.0 s? A) 52 m's B) 39 m's C) 46 m's D) 33 m's E) 43 m/s

Explanation / Answer

1)Resolving forces in x(unit vector i) and y(unit vector j) directions:

65 N force F1 = 65cos(30) i + 65sin(30) j = 56.29 i + 32.5 j

Similarly F2 = - 30 i

and F3 = -20sin(20) i - 20cos(20) j = -6.84 i - 18.79 j

F1 + F2 + F3 = 19.45 i + 13.71 j

Magnitude = sqrt ( 19.45^2 + 13.71^2) = 23.8 N (D)

2) Direction of resultant = atan(13.71/19.45) = 35 degrees with positive x axis (A)

3) a) it is at 35 degrees to x axis

4) v^2 - u^2 = 2*a*s

acceleration a = (220^2 - 387^2)/2/0.14 = -362032 m/s^2 = 362.03 km/s^2 (option B)

where,

v=final speed, 220m/s,

u = initial speed,387 m/s

, s = displacement(14 cm)

5) u = 16 i - 12 j

a = 3 i - 6 j

v = u + a*t = 16 i - 12 j + 2*(3 i - 6 j) = 22 i - 24 j

Magnitude(v) = sqrt(22^2+24^2) = 32.55 ~ 33 m/s (option D)

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