Part A A delivery company has unloaded a \( 30 \mathrm{~kg} \) crate in your driveway. The coefficient of static friction between the crate and the driveway surface is \( \mu_{\mathrm{s}}=0.40 \). The coefficient of kinetic friction is \( \mu_{\mathrm{k}}=0.30 \). In order to move the crate, you apply a horizontal force of magnitude \( F \) by pushing on it. As a result, the crate slides with an acceleration of \( 2.0 \mathrm{~m} / \mathrm{s}^{2} \). What is the force \( F \) ? Express your answer with the appropriate units.
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(I) If the coefficient of kinetic friction between a 22-kg crate and the floor is 0.30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_k$ is zero?
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Problems Involving Friction, Inclines
A 20 kg crate is subject to a force having a constant direction and magnitude of F = 100 N at 30 degree from the horizontal. The crate is moving to the right with an initial speed of 8 m/s. The coefficient of kinetic friction between the crate and the ground is μk = 0.25. a) Draw the free body diagram of the crate. [2 marks] b) Using Newton’s Laws of motion, determine the speed of the crate when it is moved a distance, s = 21 m, [4 marks] c) Using energy conservation law, recalculate its speed when s=21 m. [4 marks]
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