Two workers are moving a slab of ice (m = 290 kg) across the factory floor. As seen from above, one worker exerts a force of 415 N at an angle of -20o, and the other exerts a force of 470 N at an angle of 50o. What is the magnitude of the acceleration of the ice slab?
Fr = 415[-20o] + 470[50o].
Fr = (415*Cos(-20)+470*Cos50) +
(415*sin(-20)+470*sin50).
Fr = (390+302) + (-142+360)i.
Fr = 692 + 218i = 726N[17.5o].
Fr = M*a; a = Fr/M = 726[17.5]/290 = 2.50m/s^2[17.5o].
To find the magnitude of the acceleration of the ice slab, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
First, let's break down the forces exerted by each worker into their horizontal and vertical components.
The horizontal component of a force can be determined by multiplying the force magnitude by the cosine of the angle, and the vertical component can be determined by multiplying the force magnitude by the sine of the angle.
For the first worker:
- Horizontal component = 415 N * cos(-20°)
- Vertical component = 415 N * sin(-20°)
For the second worker:
- Horizontal component = 470 N * cos(50°)
- Vertical component = 470 N * sin(50°)
Next, we need to sum up the horizontal and vertical components of the forces to find the net force along each axis.
Horizontal net force = sum of the horizontal components of the forces
Vertical net force = sum of the vertical components of the forces
Once we have the net force, we can calculate the acceleration using the formula:
acceleration = net force / mass
By substituting the values into the equations, we can find the magnitude of the acceleration of the ice slab.