Madison pushes with a 160-N horizontal force on a 20-kg crate of coffee resting on a warehouse floor. The force of friction on the crate is 80 N. Show that the acceleration is 4 m/s2.
F=160 N
m=20 kg
Ffr=80 N
Net force causing acceleration = 160-80
=80 N
Use Newton's second law,
F=ma
a=F/m
=80/20
=4 m/s²
Well, let me calculate that for you while I put on my clown shoes for some mathematical fun!
According to Newton's second law, F = ma, where F is the applied force, m is the mass, and a is the acceleration.
So in this case, the applied force is 160 N, and the mass is 20 kg. And since we're trying to find the acceleration, we'll substitute it with "a".
Now, we have a slight challenge here because we need to take into account the force of friction acting in the opposite direction. But don't worry, I'm an expert at clown dancing our way through equations!
The force of friction is given as 80 N. So the equation for the net force on the crate becomes:
Net force = Applied force - Force of friction
Net force = 160 N - 80 N
Net force = 80 N
Okay, now let's substitute the values we have into Newton's second law equation:
80 N = 20 kg * a
To find the acceleration, we can rearrange the equation as:
a = 80 N / 20 kg
a = 4 m/s²
Ta-da! We did it! The acceleration is indeed 4 m/s². Now, if you'll excuse me, I'll go practice my clown somersaults!
To determine the acceleration of the crate, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
The given information is as follows:
- Applied horizontal force (F) = 160 N
- Frictional force (F_friction) = 80 N
- Mass of the crate (m) = 20 kg
1. Calculate the net force acting on the crate.
Net force (F_net) = Applied force - Frictional force
= F - F_friction
= 160 N - 80 N
= 80 N
2. Calculate the acceleration of the crate.
Acceleration (a) = F_net / m
= 80 N / 20 kg
= 4 m/s^2
Therefore, the acceleration of the crate is 4 m/s^2.
To show that the acceleration is 4 m/s^2, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
The net force acting on the crate can be calculated by subtracting the force of friction from the applied force. So, the net force (F_net) is given by:
F_net = Applied force - Force of friction
= 160 N - 80 N
= 80 N
Now, we can use Newton's second law of motion, which states that:
F_net = mass * acceleration
Rearranging the equation, we have:
acceleration = F_net / mass
Plugging in the given values:
acceleration = 80 N / 20 kg
= 4 m/s^2
Therefore, the acceleration of the crate is indeed 4 m/s^2.