A worker drags a crate across a factory floor by pulling on a rope tied to the crate. The worker exerts a force of 450 N on the rope, which is inclined at 38° to the horizontal, and the floor exerts a horizontal force of 125 N that opposes the motion. Calculate the acceleration of the crate if its mass is 331 kg and calculate the acceleration of the crate if its weight is 331 N.
The upward force the rope exerts is 450*sin38. The horizontal force is 450 cos38
Horizontal forces= mass*acceleation
450cos38 - 125- mass*acceleraiton
calcuate acceleration. Mass=weighcrate/g
To calculate the acceleration of the crate, we need to find the net force acting on it using Newton's second law, F=ma. In this case, the net force is the difference between the force applied by the worker and the opposing force exerted by the floor.
1. When the mass of the crate is given as 331 kg:
First, let's calculate the net horizontal force acting on the crate:
Net horizontal force = force applied - opposing force
= (450 N * cos(38°)) - 125 N
Now, we can use Newton's second law to find the acceleration:
Acceleration = net horizontal force / mass
= (450 N * cos(38°)) - 125 N / 331 kg
2. When the weight of the crate is given as 331 N:
Since the weight of an object is equal to the mass multiplied by the acceleration due to gravity (w=mg), we can calculate the mass of the crate using the given weight:
mass = weight / acceleration due to gravity
= 331 N / 9.8 m/s^2
Now, we can use the mass calculated above to find the net horizontal force and then the acceleration:
Net horizontal force = force applied - opposing force
= (450 N * cos(38°)) - 125 N
Acceleration = net horizontal force / mass
= (450 N * cos(38°)) - 125 N / (331 N / 9.8 m/s^2)
Calculate the above expression to get the acceleration.