two people are pushing a car of mass 2000kg. if they each push with a force of 320N at an angle of 15degrees to each side of the car, calculate the acceleration of the car, assuming no resistance... please help
To calculate the acceleration of the car, we need to find the net force acting on the car. The net force is the vector sum of the individual forces exerted by the two people.
First, we need to resolve the forces into their horizontal and vertical components. Since the forces are at an angle of 15 degrees to each side of the car, we can use trigonometry to determine the horizontal and vertical components.
The horizontal component of each force is given by:
F_horizontal = F * cos(angle)
Given:
F = 320 N
angle = 15 degrees
F_horizontal = 320 * cos(15) ≈ 312.236 N
Now, since there are two people pushing, the total horizontal force exerted on the car is:
F_total_horizontal = 2 * F_horizontal = 2 * 312.236 N ≈ 624.472 N
Since there is no resistance, the horizontal force is the only force acting on the car in the x-direction. Therefore, the net force acting on the car in the x-direction is:
F_net_x = F_total_horizontal = 624.472 N
The net force in the y-direction is zero because neither person is pushing vertically, so:
F_net_y = 0 N
Now, we can use Newton's second law of motion to calculate the acceleration:
F_net = m * a
Where:
F_net is the net force
m is the mass of the car
a is the acceleration
Since F_net is the net force acting on the car, which is equal to F_net_x, we have:
F_net_x = m * a
Rewriting the equation for acceleration:
a = F_net_x / m
Given:
m = 2000 kg
a = 624.472 N / 2000 kg
Calculating the acceleration:
a = 0.312236 m/s²
Therefore, the acceleration of the car, assuming no resistance, is approximately 0.312236 m/s².
To calculate the acceleration of the car, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a).
In this case, we have two people pushing the car with a force of 320N each, at an angle of 15 degrees to each side of the car. Since the forces are acting at an angle, we need to break them down into their horizontal and vertical components.
The vertical component of each force is given by F * sin(theta), where F is the magnitude of the force and theta is the angle of the force. In this case, since the car is being pushed horizontally, the vertical components of the forces do not contribute to the acceleration.
The horizontal component of each force is given by F * cos(theta). Therefore, the total horizontal force acting on the car is 2 * (F * cos(theta)).
Now, we can calculate the acceleration of the car by dividing the total force by the mass of the car:
a = (2 * (F * cos(theta))) / m
Substituting the given values:
a = (2 * (320N * cos(15 degrees))) / 2000kg
Calculating this equation will give us the acceleration of the car assuming no resistance.