A 50 kg crate shown in fig. rest on horizontal plane for which the coefficient of kinetic friction is μ = 0.3. If the crate does not tip over when it is subjected to a 400 N force, determine the velocity of the crate in 8 sec starting from rest using…

Q.5 (B) A 50 kg crate shown in fig. rest on horizontal plane for which the coefficient of kinetic friction is μ = 0.3. If the crate does not tip over when it is subjected to a 400 N force, determine the velocity of the crate in 8 sec starting from rest using impulse momentum principle.

[Figure: crate on a horizontal floor, \(\mu_k = 0.3\); force P = 400 N pulls the crate to the right at 30° above the horizontal.]

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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Given: m = 50 kg, W = 490.5 N, P = 400 N at 30°, \(\mu_k = 0.3\), u = 0, t = 8 s.

Normal reaction (\(\sum F_y = 0\)): \(N = 490.5 - 400\sin30^\circ = 290.5\) N; friction \(F = 0.3 \times 290.5 = 87.15\) N (←).

Impulse–momentum in x-direction: \(mu + \sum F_x\,t = mv\)

\(0 + (400\cos30^\circ - 87.15)(8) = 50v \Rightarrow (346.41 - 87.15)(8) = 50v \Rightarrow 2074.1 = 50v\)

Answer: v = 41.48 m/s (to the right) after 8 s.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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A 50 kg crate shown in fig. rest on horizontal plane for which the coefficient of kinetic friction is μ = 0.3. If the crate does not tip over when it is subjected to a 400 N force, determine the velocity of the crate in 8 sec starting from rest using…

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