A worker drags a crate across a factory floor by pulling on a rope tiedto the crate. The worker exerts a force of 450 N on the rope, which is inclined at 38 degrees to the horizontal and the floor exerts a horizontal force of 125 N that opposes the motion. Calculate the magnitude of the acceleration of the crate if a)its mass is 310kg and b) its weight is 310 N.

How would I find the acceleration with the given information?

a = F/m
To get the acceleration (in m/s^2), divide the resultant force (in N) along the floor by the mass (in kg).
The resultant force along the floor is
450 N* cos 38 - 125 N

You do the rest

To find the acceleration of the crate, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.

a = F_net / m

a) First, let's calculate the net force acting on the crate. We can achieve this by subtracting the force opposing the motion from the force exerted by the worker.

F_net = 450 N * cos(38°) - 125 N

Now, let's substitute the value of F_net into the equation:

a = (450 N * cos(38°) - 125 N) / 310 kg

Calculate the value and you will find the magnitude of the acceleration of the crate in meters per second squared (m/s^2).

b) In this case, we are given the weight of the crate, which is a force. However, we need to convert it into mass in kilograms using the equation:

Weight = mass * acceleration due to gravity

310 N = mass * 9.8 m/s^2

Rearrange the equation to solve for mass:

mass = 310 N / 9.8 m/s^2

Now that we have the mass, we can use the same equation as in part a to calculate the acceleration:

a = (450 N * cos(38°) - 125 N) / (310 N / 9.8 m/s^2)

Again, calculate the value and you will find the magnitude of the acceleration of the crate in m/s^2.