A 60-kg mass sits on a level frictionless table. Two forces are applied to the mass at the same time. The first has a magnitude of 20 N and an angle of 20 degrees North of East. The second has a magnitude of 45 N and an angle of 13 degrees East of South . What is the resultant acceleration of the mass? a.) What is the net force acting on the mass? b.) what is the resultant acceleration of the mass?
To find the resultant acceleration of the mass, we need to determine the net force acting on the mass and then use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma).
a.) To find the net force acting on the mass, we need to calculate the horizontal and vertical components of each force and then add them up.
First Force (20 N at an angle of 20 degrees North of East):
- Horizontal Component: 20 N * cos(20°)
- Vertical Component: 20 N * sin(20°)
Second Force (45 N at an angle of 13 degrees East of South):
- Horizontal Component: 45 N * cos(13°)
- Vertical Component: -45 N * sin(13°) [negative because it is South]
Now, let's add up the horizontal and vertical components separately to find the net force in each direction.
Horizontal Component:
- Net Horizontal Force = Horizontal Component of First Force + Horizontal Component of Second Force
Vertical Component:
- Net Vertical Force = Vertical Component of First Force + Vertical Component of Second Force
b.) To find the resultant acceleration, we divide the net force in each direction by the mass of the object.
- Net Horizontal Acceleration = Net Horizontal Force / Mass
- Net Vertical Acceleration = Net Vertical Force / Mass
We can combine the horizontal and vertical accelerations to find the resultant acceleration using the Pythagorean theorem:
- Resultant Acceleration = √[(Net Horizontal Acceleration)^2 + (Net Vertical Acceleration)^2]
By following these steps, we can find the answers to both parts (a) and (b) of the question.