Forces F 1 and F 2 act on a mass m = 0.19 kg, as shown in the diagram below. The

Question

Forces F1 and F2 act on a mass m = 0.19 kg, as shown in the diagram below.

The magnitudes of the forces and angles are as follows:

F1 = 2.8 N, ?1 = 42 degrees

F2 = 3 N, ?2 = 57 degrees

1)What are the x and y components of the force F1?

2)What are the x and y components of the force F2?

3)What are the x and y components of the sum of these two forces (the resultant force)?

4)What is the magnitude of the resultant force?

Forces F1 and F2 act on a mass m = 0.19 kg, as shown in the diagram below. The magnitudes of the forces and angles are as follows: F1 = 2.8 N, ?1 = 42 degrees F2 = 3 N, ?2 = 57 degrees What are the x and y components of the force F1? What are the x and y components of the force F2? What are the x and y components of the sum of these two forces (the resultant force)? What is the magnitude of the resultant force? What are the x and y components of the resulting acceleration of the mass? What is the magnitude of the acceleration?

Explanation / Answer

1)x comp of F1=2.8*cos(42 degree)=2.08N

ycomp of F1=2.8*sin(42 degree)=1.873N

2)x comp of F2=3*cos(57 degree)=1.634N

y comp of F2=3*sin(57 degree)=2.516N

3)x component = 2.8*cos(42 degree)+3*cos(57 degree)=3.714N

y comp=2.8*sin(42 degree)+3*sin(57 degree)=4.39N

4)mag=sqrt(3.714^2+4.39^2)=5.75N

5)x comp=x comp of force /mass=3.714/0.19=19.54m/s2

y comp=4.39/0.19=23.10m/s2

6)mag=sqrt(19.54^2+23.1^2)=30.26m/s2

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