The diagram below shows a block of mass m = 2.00 k g on a frictionless horizonta
ID: 2275873 • Letter: T
Question
The diagram below shows a block of mass m=2.00kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F1=4N F2=6N And F3= 8N are applied to the block, initially at rest on the surface, at angles shown on the diagram. In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive).
Express your answer in degrees to two significant figures.
Express your answer in meters per second to two significant figures
Express your answer in degrees to two significant figures.
The diagram below shows a block of mass m=2.00kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F1=4N F2=6N And F3= 8N are applied to the block, initially at rest on the surface, at angles shown on the diagram. In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive). Calculate the magnitude of the total resultant force Fr= F1+F2+F3 Express your answer in Newtons to three significant figures. in N What angle does F r make with the positive x axis? Express your answer in degrees to two significant figures. What is the direction of a ? In other words, what angle does this vector make with respect to the positive x axis? Express your answer in degrees to two significant figures. How far (in meters) will the mass move in 5.0 s? Express the distance in meters to two significant figures. What is the magnitude of the velocity vector of the block at t=5.0s? Express your answer in meters per second to two significant figures In what direction is the mass moving at time t=5.0s? That is, what angle does the velocity vector make with respect to the positive xaxis? Express your answer in degrees to two significant figures.Explanation / Answer
Fr = F1+F2+F3
F1 = 4cos(25) i + 4sin(25)j
F2 = 6cos(35) i - 6sin(35)j
F3 = -8i
Fr = 4cos(25) i + 6cos(35) i -8i - 6sin(35)j + 4sin(25)j
Fr = 0.540 i - 1.75 j
Magnitude = |Fr| = sqrt(0.54^2 + 1.75^2) = 1.831 N
Angle = arctan(1.75/-1.75) = 287.15 degrees
a = Fr/m = (0.540 i - 1.75 j) * 0.5 = 0.270 i - 0.875 j
|a| = sqrt(0.27^2 + 0.875^2) = 0.916
Angle = arctan(2.566/0.270) = 287.15 degrees
S = ut + 0.5*a*t^2
S = 0 + 0.5*0.916*5^2
S = 11.45 m
v = 0+at
v = 5(0.270 i - 0.875j) = 5*0.916 = 4.580 m/s^2
Angle = arctan(5*2.566 / 5*-0.875j) = 287.15 degrees