A 1200 kg car pushes a 2100 kg truck that has a dead battery to the right. When the driver steps on the accelerator, the drive wheels of the car push against the ground with a force of 4500 N . What is the magnitude of the force the car applies to the truck?
What is the magnitude F_ct of the force that the car exerts on the truck? where the positive y direction is upward, and the positive x direction is to the right, the direction in which F_ct_vec points.
The 4500 N force on the car's tires accelerates the car and the truck together at a rate
a = 4500/(1200+2100) = 1.364 m/s
(assuming the pushed truck offers no resistance).
The force applied to the truck is is
Mtruck*a = 2864 N
The second part of your question seems repetitive. I do not understand your notation.
Well, since the car has a dead battery, it must be using some serious girl power to push the truck. Good for her! Now, let's calculate the magnitude of the force the car applies to the truck.
To do this, we need to use Newton's third law which states that for every action, there is an equal and opposite reaction. In this case, the car pushing against the ground with a force of 4500 N creates a reaction force on the car in the opposite direction.
Since the car and the truck are pushing against each other, the force that the car applies to the truck is equal in magnitude but in the opposite direction, so it's also 4500 N.
So, the magnitude F_ct of the force that the car exerts on the truck is 4500 N. Just remember, even though the truck has a dead battery, it's not dead in terms of receiving a push!
To find the magnitude of the force the car applies to the truck, we need to calculate the net force exerted by the car on the truck.
Given:
Mass of the car (m1) = 1200 kg
Mass of the truck (m2) = 2100 kg
Force exerted by the car on the ground (F_cg) = 4500 N
We can start by finding the acceleration of the car using Newton's second law:
F_cg = m1 * a
Rearranging the equation, we can calculate the acceleration of the car:
a = F_cg / m1
= 4500 N / 1200 kg
= 3.75 m/s^2
Now, we know that the car and the truck experience the same acceleration (assuming the frictional force between them is negligible). Therefore, the net force acting on the truck (F_ct) can be calculated using Newton's second law:
F_ct = m2 * a
= 2100 kg * 3.75 m/s^2
= 7875 N
So, the magnitude of the force the car applies to the truck is 7875 N.
Regarding the direction of the force (F_ct_vec), it would point in the same direction as the acceleration (to the right in this case) since the car is pushing the truck to the right.
To find the magnitude of the force that the car applies to the truck, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, the force exerted by the car on the truck is equal in magnitude but opposite in direction to the force exerted by the truck on the car.
Given:
Mass of the car (m_car) = 1200 kg
Mass of the truck (m_truck) = 2100 kg
Force exerted by the car on the ground (F_cg) = 4500 N
First, let's calculate the acceleration of the car using Newton's second law of motion:
F_cg = m_car * a_car
Rearranging the formula, we can solve for the acceleration (a_car):
a_car = F_cg / m_car
Substituting the given values:
a_car = 4500 N / 1200 kg
≈ 3.75 m/s^2
Now that we have the acceleration of the car, we can calculate the force the car applies to the truck.
To find the magnitude of the force (F_ct) that the car exerts on the truck, we need to use Newton's second law, which states that force is equal to the mass of an object multiplied by its acceleration:
F_ct = m_truck * a_car
Substituting the given values:
F_ct = 2100 kg * 3.75 m/s^2
≈ 7875 N
Therefore, the magnitude of the force that the car exerts on the truck (F_ct) is approximately 7875 N.