2. An elephant is pushing, with 75 000 N of force, on two jeeps that are stuck in the mud. The elephant pushes on the first jeep (which is 2000 kg (2 SD)) and it, in turn, pushes on the second jeep (which is 1500 kg). The co-efficient of friction between the jeeps and the mud is 1.9.
a)Determine the acceleration of the jeeps.
b)Determine the force that the heavier jeep exerts on the lighter jeep.
To determine the acceleration of the jeeps, 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 (F = ma).
a) First, let's find the net force exerted on the first jeep by the elephant. This net force can be calculated by subtracting the force of friction from the force exerted by the elephant.
Net force on the first jeep = Force exerted by elephant - Force of friction
Net force on the first jeep = 75,000 N - (coefficient of friction * weight of the first jeep)
Since weight = mass * acceleration due to gravity, we can rewrite the formula as:
Net force on the first jeep = 75,000 N - (1.9 * mass of first jeep * acceleration due to gravity)
The mass of the first jeep is 2000 kg, and acceleration due to gravity is approximately 9.8 m/s^2.
Net force on the first jeep = 75,000 N - (1.9 * 2000 kg * 9.8 m/s^2)
Now we can find the net force on the first jeep.
Net force on the first jeep = 75,000 N - 36,960 N
Net force on the first jeep = 38,040 N
Next, we can find the net force exerted by the first jeep on the second jeep. This net force is equal to the force exerted by the elephant minus the force of friction between the jeeps.
Net force on the second jeep = Force exerted by first jeep - Force of friction between the jeeps
Net force on the second jeep = 38,040 N - (coefficient of friction * weight of the second jeep)
The mass of the second jeep is 1500 kg.
Net force on the second jeep = 38,040 N - (1.9 * 1500 kg * 9.8 m/s^2)
Now we can find the net force on the second jeep.
Net force on the second jeep = 38,040 N - 27,540 N
Net force on the second jeep = 10,500 N
Since the net force is the same for both jeeps (according to Newton's third law of motion), we can conclude that the acceleration of both jeeps is the same.
Net force = mass * acceleration
10,500 N = (2000 kg + 1500 kg) * acceleration
10,500 N = 3500 kg * acceleration
Now we can solve for acceleration.
acceleration = 10,500 N / 3500 kg
acceleration = 3 m/s^2
Therefore, the acceleration of the jeeps is 3 m/s^2.
b) To determine the force that the heavier jeep exerts on the lighter jeep, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
According to this law, the force exerted by the heavier jeep on the lighter jeep is equal in magnitude but opposite in direction to the net force on the lighter jeep.
Force exerted by the heavier jeep on the lighter jeep = Net force on the second jeep
Force exerted by the heavier jeep on the lighter jeep = 10,500 N
Therefore, the force that the heavier jeep exerts on the lighter jeep is 10,500 N.
a) To determine the acceleration of the jeeps, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a). Mathematically, this can be represented as:
F = m * a
In this scenario, the force pushing on the first jeep is 75,000 N. The mass of the first jeep is 2,000 kg. Plugging these values into the equation, we get:
75,000 N = 2,000 kg * a
To find the acceleration, we need to isolate the variable "a". We can do this by dividing both sides of the equation by the mass:
a = 75,000 N / 2,000 kg
Simplifying the equation, we find:
a = 37.5 m/s^2
Therefore, the acceleration of the jeeps is 37.5 m/s^2.
b) To determine the force that the heavier jeep exerts on the lighter jeep, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The force exerted on the lighter jeep by the heavier jeep is equal in magnitude but opposite in direction to the force exerted on the heavier jeep by the lighter jeep.
Since the force pushing the first jeep is 75,000 N and the mass of the second jeep is 1,500 kg, we can find the force exerted by the second jeep using the equation:
F = m * a
Plugging in the values, we get:
F = 1,500 kg * 37.5 m/s^2
Simplifying the equation, we find that the force exerted by the second jeep is:
F = 56,250 N
Therefore, the force that the heavier jeep exerts on the lighter jeep is 56,250 N.