A 200kg crate us pushed horizontally with a force of 700 N. If the coefficient of friction is 0.20, calculate the acceleratio of the crate.
I tried doing this but I don't seem to be getting the right answer.
m = 200 kg
f(app)= 700 N
U = 0.20
Ff = (0.20)(200)(-9.81)
=-392.4 N
Fnet = 700-(-392.4)
= 1092.4 N
Fnet = mass x acceleration
1092.4 = 200 (a)
5.462 m/s^2 = a
The answer booklet says that I should be getting 3.3m/s^2 as my answer.
Well, it seems like the crate is quite stubborn and doesn't want to move as fast as you'd like it to. Maybe it's just having a lazy day. But fear not, I'm here to help you out!
Let's start from the beginning. You're correct in using the formula Ff = (U)(m)(g) to calculate the force of friction, where U is the coefficient of friction, m is the mass, and g is the acceleration due to gravity.
Plugging in the values, we have Ff = (0.20)(200)(9.81) = 392.4 N (positive because the frictional force acts in the opposite direction to the force applied).
Now, to find the net force (Fnet), we need to subtract the force of friction from the applied force: Fnet = 700 - 392.4 = 307.6 N.
Finally, using the equation Fnet = m(a), we can solve for acceleration (a): a = Fnet / m = 307.6 / 200 = 1.538 m/s^2.
Ah, I'm sorry if that answer doesn't match the one in the booklet. Maybe the crate was just in a particularly energetic mood that day and decided to defy the laws of physics. Keep practicing, and remember that sometimes the answers in books can be a bit too serious for their own good!
Your calculations are correct. The acceleration of the crate should indeed be 5.462 m/s^2. It seems that there might be an error in the answer booklet or in the way the problem is stated. Make sure to double-check your calculations and assumptions.
To calculate the acceleration of the crate, you need to consider the net force acting on it. The net force is the difference between the applied force and the force of friction.
In this case, the applied force is 700 N and the coefficient of friction is 0.20. The force of friction can be calculated using the formula:
Force of friction = coefficient of friction * normal force
The normal force is the force exerted by the surface on the crate, which is equal to the weight of the crate when it is on a horizontal surface. The weight of the crate can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the mass of the crate is 200 kg and the acceleration due to gravity is approximately 9.81 m/s^2, we can calculate the weight:
Weight = 200 kg * 9.81 m/s^2 = 1962 N
Now we can calculate the force of friction:
Force of friction = 0.20 * 1962 N = 392.4 N
The net force acting on the crate is the applied force minus the force of friction:
Net force = 700 N - 392.4 N = 307.6 N
Finally, we can use Newton's second law of motion (F = m * a) to find the acceleration:
307.6 N = 200 kg * a
a = 307.6 N / 200 kg = 1.54 m/s^2
Therefore, the correct answer is 1.54 m/s^2, not 3.3 m/s^2 as mentioned in the answer booklet.
You should add forces to get net force
netforce=plied+friction and then fricion force is a negative, so
netforce=700-392.4