A 5.0-kg block accelerates at 0.80 m/s2 along a horizontal surface when a forward horizontal 12.0-N force acts on it. Show that the force of friction on the block is 8.0 N
12-Ff = M*a.
12-Ff = 5*0.8.
Ff =
Well, well, well, looks like we have ourselves a classic physics problem! Let's dive right in, shall we?
So we have a 5.0-kg block that's experiencing an acceleration of 0.80 m/s^2 when a 12.0-N force is applied to it. Now, we're supposed to find the force of friction acting on the block.
To do that, we need to first calculate the net force acting on the block. Newton's second law says that the net force is equal to the mass of the object multiplied by its acceleration. In this case, the mass is 5.0 kg and the acceleration is 0.80 m/s^2.
So, the net force is given by:
net force = mass × acceleration
= 5.0 kg × 0.80 m/s^2
= 4.0 N
Now, we know that there is a 12.0-N force acting on the block, which means the force of friction must be opposing it and balancing out the rest. So, the force of friction is:
force of friction = 12.0 N - 4.0 N
= 8.0 N
And voila! We've shown that the force of friction on the block is indeed 8.0 N. Aren't physics problems just a roller coaster of fun?
To find the force of friction on the block, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
The net force acting on the block is the sum of the applied force and the force of friction. In this case, the applied force is 12.0 N.
So, the net force (F_net) is given by:
F_net = 12.0 N
The mass of the block (m) is 5.0 kg.
The acceleration of the block (a) is 0.80 m/s^2.
Therefore, using Newton's second law, we have:
F_net = m * a
12.0 N = 5.0 kg * 0.80 m/s^2
Simplifying the equation:
12.0 N = 4.0 kg * (2.0 m/s^2)
Now, we know that the force of friction (F_friction) is equal to the applied force (F_applied) minus the net force (F_net). In this case, the applied force is 12.0 N, as calculated previously.
So, the force of friction is:
F_friction = F_applied - F_net
F_friction = 12.0 N - 4.0 kg * (2.0 m/s^2)
F_friction = 12.0 N - 8.0 N
Therefore, the force of friction on the block is 8.0 N.
To show that the force of friction on the block is 8.0 N, we can use Newton's second law of motion:
F_net = m * a
Where:
F_net is the net force acting on the object,
m is the mass of the object,
a is the acceleration of the object.
In this case, the net force acting on the block is the vector sum of the applied force (12.0 N) and the force of friction (F_friction).
F_net = F_applied + F_friction
Substituting the given values:
F_net = 12.0 N + F_friction
m = 5.0 kg
a = 0.80 m/s²
Now, we rearrange Newton's second law to solve for F_friction:
F_friction = F_net - F_applied
Substituting the values:
F_friction = m * a - F_applied
F_friction = 5.0 kg * 0.80 m/s² - 12.0 N
F_friction = 4.0 N - 12.0 N
F_friction = -8.0 N
It appears that the force of friction is -8.0 N, but this negative sign indicates the direction of the force. Since the question asks for the magnitude of the force, we ignore the negative sign. Thus, the force of friction on the block is 8.0 N.