An crate weighing 576 N is resting on a plane inclined 29¡Æ above the horizontal. The magnitude of the acceleration (ignore friction) is1 m/s2.
After 5.00 s, how fast will the crate be moving?
"The magnitude of the acceleration (ignore friction) is1 m/s2.
After 5.00 s, how fast will the crate be moving?"
What is 5*1?
Oh. That was easy... Thank you!!
You're welcome!
To find the speed of the crate after 5.00 s, we need to first find the distance it travels during this time period.
The crate is resting on an inclined plane, so we need to split the weight of the crate into two components: one perpendicular to the plane and one parallel to the plane.
The perpendicular component (force normal) can be found using the formula:
Force normal = weight * cos(θ)
Where weight is 576 N (given) and θ is the angle of the inclined plane (29 degrees in this case).
Force normal = 576 N * cos(29 degrees)
Force normal = 514.078 N
The parallel component (force parallel) can be found using the formula:
Force parallel = weight * sin(θ)
Force parallel = 576 N * sin(29 degrees)
Force parallel = 288.587 N
Since there is no friction mentioned in the problem, the only force acting on the crate parallel to the inclined plane is the force due to acceleration (ma).
Force parallel = ma
288.587 N = m * 1 m/s^2
Now we can solve for the mass (m):
m = 288.587 N / 1 m/s^2
m = 288.587 kg
We can use this mass to calculate the distance the crate travels during 5.00 s using the formula:
Distance = initial velocity * time + (1/2) * acceleration * time^2
Since the crate starts from rest, the initial velocity is 0 m/s.
Distance = (1/2) * acceleration * time^2
Distance = (1/2) * 1 m/s^2 * (5.00 s)^2
Distance = 12.5 m
Now we have the distance traveled during 5.00 s.
To find the final velocity, we can use the formula:
Final velocity = initial velocity + acceleration * time
Since the initial velocity is 0 m/s, the equation simplifies to:
Final velocity = acceleration * time
Final velocity = 1 m/s^2 * 5.00 s
Final velocity = 5.00 m/s
Therefore, after 5.00 s, the crate will be moving at a speed of 5.00 m/s.