A firefighter of mass 39 kg slides down a vertical pole with an acceleration of 3 m/s^2.
The acceleration of gravity is 10 m/s^2.
What is the friction force that acts on him?
Answer in units of N.
F = m a
mg - Ffriction = m (3)
so
F friction = m(g-3)
= 39 (7)
= 273 Newtons
Well, well, well, looks like we have a sliding firefighter here! And we need to find the friction force acting on him. Let's see what we can do.
Now, my dear friend, we know the firefighter's mass is 39 kg and the acceleration is 3 m/s^2. But what about gravity? Well, we can never forget about gravity, can we? It's always trying to bring us down!
The acceleration due to gravity is a whopping 10 m/s^2. So, as the firefighter slides down the pole, the force of gravity is pulling him downward with a force of F_gravity = m * g.
But wait, there's more! Since the firefighter is speeding up, we know that there must be another force in play to help him slide down faster. And that, my friend, is the friction force!
If we assume that the friction force is in the opposite direction to the firefighter's motion, we can use Newton's second law, F_net = m * a, to find the friction force.
F_net = F_gravity - F_friction
Since the firefighter is accelerating downwards, the net force is the difference between the force of gravity and the friction force.
Now, we know the gravitational force F_gravity = m * g, which means F_gravity = 39 kg * 10 m/s^2.
So, let's plug in the numbers and solve for F_friction:
F_net = m * a
F_gravity - F_friction = m * a
(39 kg * 10 m/s^2) - F_friction = (39 kg * 3 m/s^2)
Now, we can solve for F_friction:
F_friction = (39 kg * 10 m/s^2) - (39 kg * 3 m/s^2)
F_friction = 390 N - 117 N
F_friction = 273 N
So, my dear friend, the friction force that acts on the sliding firefighter is 273 N. Keep on sliding and stay safe!
To find the friction force acting on the firefighter, we'll first need to calculate the gravitational force acting on the firefighter.
The gravitational force (weight) can be calculated using the formula:
F_gravity = mass * acceleration due to gravity
Given:
Mass of the firefighter (m) = 39 kg
Acceleration due to gravity (g) = 10 m/s^2
Plugging in the values:
F_gravity = 39 kg * 10 m/s^2 = 390 N
Now, we need to calculate the net force acting on the firefighter as he slides down the pole.
The net force can be calculated using Newton's second law of motion:
Net force (F_net) = mass * acceleration
Given:
Mass of the firefighter (m) = 39 kg
Acceleration (a) = 3 m/s^2 (sliding down, so it's positive)
Plugging in the values:
F_net = 39 kg * 3 m/s^2 = 117 N
Since the friction force acts in the opposite direction to the motion of the firefighter, the friction force is equal in magnitude to the net force but opposite in direction.
Therefore, the friction force acting on the firefighter is 117 N in the upward direction.
To find the friction force acting on the firefighter, we need to consider the forces acting on him while he is sliding down the pole.
First, let's determine the gravitational force acting on the firefighter. We can use the formula:
Gravitational Force = mass * acceleration due to gravity
Given that the mass of the firefighter is 39 kg and the acceleration due to gravity is 10 m/s^2, we can substitute these values into the formula:
Gravitational Force = 39 kg * 10 m/s^2 = 390 N
Next, we need to determine the net force acting on the firefighter. The net force is the vector sum of all the forces acting on him. In this case, the net force is equal to the product of the firefighter's mass and his acceleration:
Net Force = mass * acceleration
Given that the mass of the firefighter is 39 kg and the acceleration is 3 m/s^2, we can substitute these values into the formula:
Net Force = 39 kg * 3 m/s^2 = 117 N
Since the firefighter is sliding down the pole with an acceleration of 3 m/s^2, and the only other force acting on him besides gravity is the friction force, we can determine the friction force by subtracting the gravitational force from the net force:
Friction Force = Net Force - Gravitational Force
Friction Force = 117 N - 390 N = -273 N
The negative sign indicates that the friction force is acting in the opposite direction of the net force, which means it is acting upwards. However, since frictional forces cannot be negative, we take the magnitude of the force:
Friction Force = | -273 N | = 273 N
Therefore, the friction force that acts on the firefighter is 273 N.