Answer :
To calculate the magnitude of the frictional force that stops a sliding crate, we use the equation of motion to find the acceleration and then apply Newton's second law. The calculated magnitude of the frictional force is 82.1 N.
Calculating the Magnitude of the Frictional Force
To find the magnitude of the frictional force acting on the crate, we need to use the concepts of kinetic friction and Newton's second law of motion.
The frictional force can be calculated knowing the mass of the crate, its initial speed, and the time it takes to stop due to the frictional force.
We will use the formula for force based on Newton's second law, which is F = ma, where F is the force, m is the mass, and a is the acceleration.
To find the acceleration, we use the equation of motion: v = u + at, where:
- v is the final velocity (0 m/s, since the crate stops)
- u is the initial velocity (9.02 m/s)
- a is the acceleration
- t is the time (6.49 s)
Rearranging the equation to solve for a, we have a = (v - u) / t.
Now we can calculate the acceleration: a = (0 - 9.02 m/s) / 6.49 s = -1.39 m/s².
The negative sign indicates that the crate is decelerating.
We substitute the acceleration and mass into Newton's second law to find the frictional force:
F = ma = (59.1 kg)(-1.39 m/s²) = -82.1429 N. The magnitude of the frictional force is therefore 82.1429 N, which we can round to 82.1 N.
