Question

a dockworker applies a constant horizontal force of 88.0 n to a block of ice on a smooth horizontal floor. the frictional force is negligible. the block starts from rest and moves a distance 13.0 m in a time of 4.60 s. you may want to review (page). for general problem - solving tips and strategies for this topic, you may want to view a video tutor solution of determining force from acceleration. what is the mass of the block of ice? express your answer in kilograms. view available hint(s) m = \boxed{} kg

Explanation:

Step1: Find acceleration using kinematic equation

The block starts from rest (\(u = 0\)), distance \(s = 13.0\space m\), time \(t = 4.60\space s\). Use \(s=ut+\frac{1}{2}at^{2}\). Since \(u = 0\), \(s=\frac{1}{2}at^{2}\). Solve for \(a\):
\(a=\frac{2s}{t^{2}}\)
Substitute \(s = 13.0\space m\), \(t = 4.60\space s\):
\(a=\frac{2\times13.0}{(4.60)^{2}}=\frac{26.0}{21.16}\approx1.2287\space m/s^{2}\)

Step2: Use Newton's second law (\(F = ma\)) to find mass

Given \(F = 88.0\space N\), \(a\approx1.2287\space m/s^{2}\). Rearrange \(F = ma\) to \(m=\frac{F}{a}\).
Substitute values:
\(m=\frac{88.0}{1.2287}\approx71.6\space kg\)

Answer:

\(\approx 71.6\space kg\)