A dragster and driver together have mass 929.4 kg. The dragster, starting from rest, attains a speed of 26.5 m/s in 0.55s.
Assume the driver has a mass of 77.4 kg. What horizontal force does the seat exert on the driver? Answer in units of N.
To find the horizontal force exerted by the seat on the driver, we can use Newton's second law of motion:
force = mass × acceleration
Here, the acceleration is the change in velocity divided by the time taken to reach that velocity.
Given:
Mass of the dragster and driver = 929.4 kg
Mass of the driver = 77.4 kg
Final velocity = 26.5 m/s
Time taken = 0.55 s
To find the initial velocity, we can use the equation:
final velocity = initial velocity + (acceleration × time)
Rearranging this equation, we can find the initial velocity:
initial velocity = final velocity - (acceleration × time)
Substituting the given values:
initial velocity = 26.5 m/s - (acceleration × 0.55 s)
Since the dragster starts from rest, the initial velocity is 0 m/s. Therefore, we can solve for the acceleration:
0 = 26.5 m/s - (acceleration × 0.55 s)
Rearranging the equation, we have:
acceleration × 0.55 s = 26.5 m/s
Dividing both sides by 0.55 s:
acceleration = 26.5 m/s / 0.55 s
acceleration = 48.182 m/s²
Now, we can find the total force acting on the dragster and driver:
force = mass × acceleration
force = (929.4 kg + 77.4 kg) × 48.182 m/s²
force = 1006.8 kg × 48.182 m/s²
force = 48436.8 kg·m/s²
Since force is measured in Newtons (N), we can convert this value to Newtons by using the definition of Newton:
1 N = 1 kg·m/s²
Therefore, the horizontal force exerted by the seat on the driver is 48436.8 N.
To find the horizontal force exerted on the driver by the seat, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the driver is experiencing a horizontal acceleration as the dragster speeds up.
First, let's calculate the acceleration of the dragster. We can use the formula:
acceleration = (final velocity - initial velocity) / time
Given:
Initial velocity (u) = 0 m/s
Final velocity (v) = 26.5 m/s
Time (t) = 0.55 s
acceleration = (26.5 m/s - 0 m/s) / 0.55 s
acceleration = 48.18 m/s^2
Now that we have the acceleration, we can find the total force acting on the driver by using the formula:
force = mass * acceleration
Given:
Mass of dragster and driver (m) = 929.4 kg
force = 929.4 kg * 48.18 m/s^2
force = 44804.692 N
Therefore, the horizontal force exerted on the driver by the seat is approximately 44804.692 N.