1.Three forces in the x-y plane act on a 2.9 kg mass: 11.1 N directed at 20, 14.2 N directed at 131 , and 12.2 N directed at 201 . All angles are measured from the positive x-axis, with positive angles in the Counter-Clockwise direction. Calculate the magnitude of the acceleration.
Calculate the direction of the resultant force using the same sign convention as above in degrees
2.A person walks on level ground 0.7 km east, then 300 meters south, and then climbs to the top of the Washington Monument (height 180 meters). What is the net displacement of the person?
3.Calculate the normal force exerted on a 2.81 kg book resting on a surface inclined at 32.2 above the horizontal
The distance between intital and final locations is the square root of the sum of the squares of the three movements, since they are are perpendicalar to one another.
In meters, that would be
sqrt[(700)^2 + (300)^2 + (180)^2] = ?
Please show your work and avoid multiple posts.
procedure of inverse square fpr ligth
1. To calculate the magnitude of the acceleration, we need to find the net force acting on the 2.9 kg mass using vector addition.
First, we need to resolve the three forces into their x and y components:
- Force 1: 11.1 N at 20 degrees:
- F1x = 11.1 N * cos(20 degrees)
- F1y = 11.1 N * sin(20 degrees)
- Force 2: 14.2 N at 131 degrees:
- F2x = 14.2 N * cos(131 degrees)
- F2y = 14.2 N * sin(131 degrees)
- Force 3: 12.2 N at 201 degrees:
- F3x = 12.2 N * cos(201 degrees)
- F3y = 12.2 N * sin(201 degrees)
Next, we sum up the x and y components of the forces:
- Net Fx = F1x + F2x + F3x
- Net Fy = F1y + F2y + F3y
Now, we can use Newton's second law, F = ma, to find the acceleration:
- Net F = sqrt((Net Fx)^2 + (Net Fy)^2)
- a = Net F / mass
Plug in the values to calculate the magnitude of the acceleration.
To calculate the direction of the resultant force, we can use trigonometry to find the angle of the net force vector:
- Angle = atan(Net Fy / Net Fx)
Note: The atan function provides the angle in radians. To convert it to degrees, you can use the formula: Angle_degrees = Angle_radians * (180/pi)
Plug in the values to calculate the direction of the resultant force in degrees.
2. To find the net displacement of the person, we need to calculate the vector sum of the individual displacements.
The person initially walks 0.7 km east, which can be represented as a displacement vector:
- Displacement 1: 0.7 km east = 0.7 km * (1, 0)
Next, the person walks 300 meters south, which can also be represented as a displacement vector:
- Displacement 2: 300 m south = 0.3 km * (0, -1)
Finally, the person climbs to the top of the Washington Monument, which adds a vertical displacement:
- Displacement 3: 180 m upwards = 0.18 km * (0, 1)
To find the net displacement, we sum up the three displacements:
- Net displacement = Displacement 1 + Displacement 2 + Displacement 3
Sum up the x and y components of the displacement vectors to calculate the net displacement.
3. To calculate the normal force exerted on the book, we need to consider the vertical forces acting on it.
First, we can resolve the force of gravity into its components:
- Weight = mass * gravitational acceleration
- Weight_x = 0 (since the book is on an inclined surface, the weight force acts vertically downward, perpendicular to the incline)
- Weight_y = weight * sin(incline angle)
Next, we need to calculate the force that counteracts the vertical component of the weight force, which is the normal force. The normal force is perpendicular to the incline surface:
- Normal force = weight_y
Plug in the values, considering the incline angle, to calculate the normal force exerted on the book.