Question

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1. a tugboat pulls a massive barge with a constant net force of 10,000 n. if the barge accelerates at a rate of 0.05 m/s², what is the total mass of the barge?

given:
unknown:
equation:
substitute
solve (answer with units):

Explanation:

Step1: Identify given and unknown

Given: \(F = 10000\ \text{N}\), \(a=0.05\ \text{m/s}^2\). Unknown: \(m\). Equation: \(F = ma\) (Newton's second law).

Step2: Rearrange the formula for mass

From \(F = ma\), we can solve for \(m\) as \(m=\frac{F}{a}\).

Step3: Substitute values

Substitute \(F = 10000\ \text{N}\) and \(a = 0.05\ \text{m/s}^2\) into \(m=\frac{F}{a}\), so \(m=\frac{10000}{0.05}\).

Step4: Calculate the mass

\(m=\frac{10000}{0.05}=200000\ \text{kg}\).

Answer:

Given: \(F = 10000\ \text{N}\), \(a = 0.05\ \text{m/s}^2\). Unknown: \(m\). Equation: \(F=ma\). Substitute: \(m=\frac{10000}{0.05}\). Solve: \(m = 200000\ \text{kg}\)