A 3kg mass is observed to accelerate 20m/s^2, 20 (degrees). Two forces act on the object. One force is 4.5N, 45 (degrees). Find the other force.
To find the other force acting on the object, we first need to determine the components of the given force and the resulting acceleration.
1. Resolve the given force into its horizontal and vertical components using trigonometric functions:
Horizontal component (Fx) = Force * cos(angle)
Vertical component (Fy) = Force * sin(angle)
For the given force of 4.5N at 45 degrees:
Fx = 4.5N * cos(45 degrees)
Fy = 4.5N * sin(45 degrees)
Fx ≈ 3.18N
Fy ≈ 3.18N
2. Determine the net force acting on the object by calculating the difference between the acceleration and the known force components:
Net force in the horizontal direction = Fx - other force component
Net force in the vertical direction = Fy - weight component
We know that the weight of the object can be calculated as:
Weight = mass * acceleration due to gravity (g)
The mass of the object is given as 3kg.
The acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 3kg * 9.8 m/s^2
≈ 29.4N
Net force in the vertical direction = Fy - weight
Net force in the horizontal direction = Fx - other force component
The given object is observed to accelerate at 20m/s^2 vertically. Therefore:
Net force in the vertical direction = mass * vertical acceleration
Net force in the vertical direction = 3kg * 20m/s^2
3. Equating the vertical and horizontal components of the net force equation, we can solve for the other force component:
Fy - weight = mass * vertical acceleration
Fy - 29.4N = 3kg * 20m/s^2
Solve for Fy:
Fy = 3kg * 20m/s^2 + 29.4N
Fy ≈ 89.4N
4. Finally, substitute the calculated value of Fy into the horizontal net force equation to solve for the other force component:
Fx - other force component = net force in the horizontal direction
3.18N - other force component = net force in the horizontal direction
Fx - other force component = 0 (since no horizontal acceleration is mentioned)
3.18N - other force component = 0
Solve for the other force component:
other force component ≈ 3.18N
Therefore, the other force acting on the object is approximately 3.18N.