How much force must a weight lifter apply to a 97 kg barbell to accelerate it upward from rest a distance of 85cm in 3.0 secs? Step by step instructions if possible please. I really need help.
To calculate the force needed to accelerate the barbell, you can use Newton's second law of motion, which states that the force (F) applied to an object is equal to the mass (m) of the object multiplied by its acceleration (a).
1. Determine the mass (m) of the barbell: Given as 97 kg.
2. Calculate the acceleration (a) of the barbell: Use the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the time taken. In this case, the barbell starts from rest, so the initial velocity (v₀) is 0 m/s, and the final velocity (v) can be calculated using the formula v = Δd / Δt, where Δd is the change in distance. Given that the barbell moves a distance of 85 cm (or 0.85 m) in 3.0 seconds, you have:
Δd = 0.85 m
Δt = 3.0 s
v = Δd / Δt = 0.85 m / 3.0 s ≈ 0.283 m/s
Finally, the acceleration is:
a = Δv / Δt = (v - v₀) / Δt = (0.283 m/s - 0 m/s) / 3.0 s ≈ 0.094 m/s²
3. Substitute the known values into Newton's second law to calculate the force (F):
F = m * a = 97 kg * 0.094 m/s² = 9.118 N
Therefore, the weight lifter needs to apply a force of approximately 9.12 N to accelerate the 97 kg barbell upward from rest a distance of 85 cm in 3.0 seconds.