A rope exerts a constant horizontal force of 203N pulling a 68-kg crate across the floor. The velocity of the crate is observed to increase from 3m/s to 5m/s in a time of 4 seconds under the influence of this force and the frictional force exerted by the floor on the crate.
What is the acceleration of the crate?
What is the total force acting upon the crate?
What is the magnitude of the frictional force acting on the crate?
a, accekeratuin=changevelociyt/time
b. net force=mass*acceleration
c. net force=203-frictionforce
What force would have to be applied to the crate by the rope in order for the crate to move with constant velocity?
To find the acceleration of the crate, we can use the formula:
acceleration = (change in velocity) / (time taken)
Given that the initial velocity (u) is 3m/s, the final velocity (v) is 5m/s, and the time taken (t) is 4 seconds, we can calculate the change in velocity:
change in velocity = v - u = 5m/s - 3m/s = 2m/s
Now we can substitute the values into the formula:
acceleration = (2m/s) / (4s) = 0.5m/s²
Therefore, the acceleration of the crate is 0.5m/s².
To find the total force acting upon the crate, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):
force = mass × acceleration
Given that the mass (m) of the crate is 68kg and the acceleration (a) is 0.5m/s², we can substitute these values into the formula:
force = 68kg × 0.5m/s² = 34N
Therefore, the total force acting upon the crate is 34N.
To find the magnitude of the frictional force acting on the crate, we need to use the fact that the net force acting on the crate is equal to the force applied by the rope minus the frictional force. This can be expressed with the formula:
net force = force applied - frictional force
Given that the force applied by the rope is 203N, and the net force acting on the crate is the force required to cause the observed acceleration, which we calculated as 34N, we can rearrange the formula to solve for the frictional force:
frictional force = force applied - net force
= 203N - 34N
= 169N
Therefore, the magnitude of the frictional force acting on the crate is 169N.