I just want somebody to check my answer on this problem please :-)
There is a box which weighs 1000 kg. There is an applied force acting upon it with a force of 20000 N (horizontally). The mu is 1.2. What is the acceleration (again, horizontally) of the object?
I got 8.24 m/s^2. Please check if this is right! If I didn't, I'll show you all the steps I took. Thank you!
If mu = 1.2, the friction force opposing motion is M g mu = 1000*9.8*1.2 = 11,760 N
The net force pulling the box is
F = 20,000 - 11,760 = 8240 N
and the acceleration is
a = F/m = 8.24 m/s^2.
Congratultions!
To check if your answer is correct, we can use Newton's second law of motion and the frictional force equation.
The equation for Newton's second law of motion is:
F = ma
where F is the net force acting on the object, m is the mass of the object, and a is the acceleration.
In this case, the net force acting on the object is the applied force minus the frictional force:
Fnet = Fapplied - Ffriction
The frictional force can be calculated using the equation:
Ffriction = μ * FN
where μ is the coefficient of friction and FN is the normal force. The normal force FN is equal to the weight of the object in this case.
Given:
- Applied force, Fapplied = 20000 N
- Weight of the object, FN = mg = 1000 kg * 9.8 m/s^2 = 9800 N
- Coefficient of friction, μ = 1.2
Let's calculate the frictional force Ffriction:
Ffriction = μ * FN
= 1.2 * 9800 N
= 11760 N
Now, let's find the net force:
Fnet = Fapplied - Ffriction
= 20000 N - 11760 N
= 8240 N
Finally, we can calculate the acceleration using Newton's second law of motion:
Fnet = ma
Rearranging the equation to solve for acceleration:
a = Fnet / m
= 8240 N / 1000 kg
= 8.24 m/s^2
So, your answer of 8.24 m/s^2 is correct! Well done!