The force required to bring a 1029 kg mass to rest from a speed of 32 m/s over a distance of 122 m is approximately 4331.72 newtons, calculated using the work-energy principle.
To calculate the force needed to bring a 1029 kg mass to rest from a velocity of 32 m/s in a distance of 122 m, we can use the work-energy principle. This principle relates the work done by the force to the change in kinetic energy. The kinetic energy (KE) of the mass is given by ½ mv², where m is the mass and v is the velocity. The work done (W) by the force to stop the mass is the force times the stopping distance (d), or W = Fd. Setting the work equal to the change in kinetic energy gives Fd = ½ mv². Rearranging the equation to solve for F gives F = (½ mv²) / d.
Substituting the provided values (m = 1029 kg, v = 32 m/s, and d = 122 m) we find that the required force is approximately:
F = (½ × 1029 kg × (32 m/s)²) / 122 m
Performing the calculation:
F = (0.5 × 1029 kg × 1024 m²/s²) / 122 m ≈ 4331.72 N
Therefore, the force needed to bring the mass to rest is approximately 4331.72 newtons.
The deceleration force required to stop a 1029 kg object traveling at 32 m/s over a distance of 122 m is approximately 4331.72 newtons.