An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 5.1 N; a second force has a magnitude of 4.3 N and points in the negative y direction. Find the direction and magnitude of the third force acting on the object.
The sum of the three force vectors must be zero since there is no acceleration.
The third force will be the equilibrant (which is minus the resultant) of the first two.
Since the first two forces are perpendicular, the equilibrant magnitude is given by the Pythagorean theorem. It is 6.67 N
When you push a 1.70 kg book resting on a tabletop it takes 2.60 N to start the book sliding. Once it is sliding, however, it takes only 1.50 N to keep the book moving with constant speed. What are the coefficients of static and kinetic friction between the book and the tabletop?
F1+F2+F3 = M*a = M*0 = 0.
5.1 - 4.3i + F3 = 0.
F3 = -5.1 + 4.3i = 6.67[40.1o] N. of W. = 139.9o CCW from +x-axis.
Wb = M*g = 1.70 * 9.8 = 16.66 N. = Normal force(Fn).
Fap-Fs = M*a = M*0 = 0.
2.6 - u*Fn = 0.
2.6 - u*16.66 = 0.
16.66u = 2.6.
u = 0.156 = Coefficient of static friction.
1.5-Fk = M*a = M*0 = 0.
1.5 - u*Fn = 0.
1.5 - u*16.66 = 0.
16.66u = 1.5.
u = 0.090 = Coefficient of kinetic friction.
To find the direction and magnitude of the third force acting on the object, we need to use the fact that the object is moving with constant velocity. This means that the net force acting on the object must be zero.
Let's break down the forces into their x and y components:
The force in the positive x direction has a magnitude of 5.1 N. Since it is in the positive x direction, its x component is 5.1 N and its y component is 0 N.
The force in the negative y direction has a magnitude of 4.3 N. Since it is in the negative y direction, its y component is -4.3 N and its x component is 0 N.
Since the object is moving with constant velocity, the net force in the x direction must be zero:
Sum of x components = 5.1 N + 0 N + x = 0 N
x = -5.1 N
Similarly, the net force in the y direction must be zero:
Sum of y components = -4.3 N + 0 N + y = 0 N
y = 4.3 N
Now, we can find the magnitude and direction of the third force using the x and y components:
Magnitude of the third force = square root of (x^2 + y^2)
= square root of ( (-5.1 N)^2 + (4.3 N)^2 )
= square root of ( 26.01 N^2 + 18.49 N^2 )
= square root of ( 44.5 N^2 )
= 6.67 N (rounded to two decimal places)
The direction of the third force can be found using the arctan function:
Direction = arctan (y/x)
= arctan (4.3 N / -5.1 N)
= -40.6 degrees (rounded to one decimal place)
Therefore, the magnitude of the third force is 6.67 N, and it points in the direction of -40.6 degrees (measured counterclockwise from the positive x-axis).