Three forces act on a 12-kg block resting on a frictionless surface as shown in
ID: 1636339 • Letter: T
Question
Three forces act on a 12-kg block resting on a frictionless surface as shown in the figure which is a top down view of the table. Find the net force acting on the block, Give your answer as a magnitude and direction with respect to the positive x-axis. Also, calculate the magnitude of the block's acceleration, F_1 = 8.0N: F_2 = 10 N: F_3 = 6.5 N Referring to the last problem, suppose the block experienced the acceleration as it traveled 0.75-m to the edge of the table and then flies off at which point only gravity acts on the block. If the table top is 0.85-m off the ground, how long would it take to hit the ground and what will be the impact speed?Explanation / Answer
1] Here let F2 points in x direction
Fx = F2 - F3 sin 120 degree = 10 - 6.5 sin 120 degree = 4.37 N
Fy = F1 + F3 cos 120 degree = 8 +6.5*-0.5 = 4.75 N
Fnet = sqrt(4.37^2+4.75^2) = 6.45 N answer
angle wrt x axis = arctan(4.75/4.37) = 47.38 degree answer
acceleration a= F/m = 6.45/12 = 0.5375 m/s^2 answer
2] time taken to fall t = sqrt(2h/g) = sqrt(2*0.85/9.8) = 0.4165 s answer
vx = sqrt(2as) = sqrt(2*0.5375*0.75) = 0.8979 m/s
vy = gt = 9.8*0.4165 = 4.0817 m/s
impact speed v = sqrt(0.8979^2+4.0817^2)
= 4.18 m/s answer