A 1300 kg car accelerates at 1.6 m/ s 2 [E]. A frictional force of 3800 N [W] is acting on the car. a) Draw the FBD of the car. b) Determine the applied force acting on the car.
a) The free-body diagram of the car can be represented as follows:
<-- Ffric -->
|
-------------
| |
| Car |
| |
-------------
|
--> Fapplied -->
Where:
- Ffric is the frictional force acting on the car (3800 N [W])
- Fapplied is the applied force on the car (unknown)
b) To determine the applied force acting on the car, we need to consider the net force acting on the car. The net force is the vector sum of all the forces acting on the car. In this case, the net force can be calculated as:
Net force = applied force - frictional force
Net force = ma (where m is the mass of the car and a is the acceleration)
Therefore, we can rewrite the equation as:
ma = Fapplied - Ffric
Solving for the applied force, we have:
Fapplied = ma + Ffric
Plugging in the given values:
Fapplied = (1300 kg)(1.6 m/s^2) + 3800 N
Fapplied = 2080 N + 3800 N
Fapplied = 5880 N
Therefore, the applied force acting on the car is 5880 N.
a) To draw the Free Body Diagram (FBD) of the car, we need to represent all the forces acting on the car.
1. First, draw a dot to represent the car's center of mass.
2. Draw an arrow pointing downward from the dot to represent the force of gravity acting on the car. This force can be represented by the symbol "mg," where m is the mass of the car and g is the acceleration due to gravity (9.8 m/s^2).
3. Draw an arrow in the opposite direction of the car's acceleration (eastward) to represent the applied force (to be determined).
4. Draw an arrow pointing leftward to represent the frictional force acting on the car.
The FBD of the car should include the following forces: the force of gravity pointing downward, the applied force pointing eastward, and the frictional force pointing leftward.
b) To determine the applied force acting on the car, we need to consider the net force on the car.
The net force is given by Newton's second law of motion: F_net = m * a, where F_net is the net force, m is the mass of the car, and a is the acceleration of the car.
Since the car is accelerating eastward, the net force is in the eastward direction. The net force can be calculated by subtracting the frictional force (opposite direction) from the applied force (eastward): F_net = F_applied - F_friction.
Setting up the equation: F_net = m * a,
F_applied - F_friction = m * a,
Substituting the values:
F_applied - 3800 N = 1300 kg * 1.6 m/s^2,
Simplifying the equation:
F_applied = 1300 kg * 1.6 m/s^2 + 3800 N.
Calculating the value:
F_applied = 2080 N + 3800 N = 5880 N.
Therefore, the applied force acting on the car is 5880 N [E].
Sure! Let's start by tackling part a) and drawing the free body diagram (FBD) of the car.
In an FBD, we represent all the forces acting on an object as vectors. In this case, the car has two forces acting on it: the frictional force and the applied force.
1. Frictional Force (3800 N [W]):
Since the frictional force is acting towards the west (left side), we can draw an arrow pointing to the left to represent this force. Label it as "F_f" to represent the frictional force.
2. Applied Force (unknown):
The applied force is the force that is causing the car to accelerate. This force is in the same direction as the acceleration, which is to the east (right side). So, draw an arrow pointing to the right and label it as "F_applied".
Now, let's move on to part b) and determine the applied force acting on the car.
To find the applied force, we can 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.
Given:
Mass of the car (m) = 1300 kg
Acceleration of the car (a) = 1.6 m/s^2 [E]
Using the formula:
Net Force = Mass × Acceleration
We can rearrange the formula to solve for the applied force:
Applied Force = Net Force / Mass
To find the net force, we need to consider the frictional force acting on the car. Since friction is a force that opposes motion, it acts in the opposite direction to the applied force.
Net Force = Applied Force - Frictional Force
Substituting the given values:
Net Force = F_applied - F_f
Now, let's plug in the values:
Net Force = F_applied - 3800 N [W]
Since the net force is equal to the mass times the acceleration, we have:
F_applied - 3800 N [W] = (1300 kg) × (1.6 m/s^2)
Now, we can isolate the applied force by adding 3800 N to both sides of the equation:
F_applied = (1300 kg) × (1.6 m/s^2) + 3800 N
Calculating the right side of the equation:
F_applied = 2080 N + 3800 N
Finally, we get:
F_applied = 5880 N
Therefore, the applied force acting on the car is 5880 N.