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A 60-N block rests on a flat surface. A horizontal force of 45 N is applied to the block. The coefficients of static and kinetic friction are 0.70 and 0.53, respectively. Will the block move, and if so, what is its acceleration? a) Yes, 2.0 m/s² b) No, 0 m/s² c) Yes, 1.5 m/s² d) No, 9.8 m/s²

User Nerdabilly
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1 Answer

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Final answer:

The block will move because the applied force exceeds the static friction force, and the block's acceleration will be approximately 2.0 m/s² after it starts moving.

The correct option is a.

Step-by-step explanation:

When determining if a block will move or not, we compare the force applied to the block to the force of static friction. The force of static friction can be calculated using the equation: friction_static = coefficient_static × normal_force. In this case, the normal force is equal to the weight of the block since the surface is flat, so the force of static friction is 0.70 × 60 N = 42 N.

Since the applied horizontal force (45 N) is greater than the force of static friction (42 N), the block will start to move. Once the block is moving, kinetic friction comes into play. The force of kinetic friction is calculated as friction_kinetic = coefficient_kinetic × normal_force = 0.53 × 60 N = 31.8 N.

To find the acceleration of the block, we use Newton's second law: acceleration = net_force / mass. The net force is the applied force minus the force of kinetic friction, which is 45 N - 31.8 N = 13.2 N. Assuming the block has a mass corresponding to a 60-N weight under standard gravity, its mass is approximately 60 N / 9.8 m/s² = 6.12 kg. Therefore, the acceleration of the block is 13.2 N / 6.12 kg ≈ 2.16 m/s², which we round to 2.0 m/s².

The correct option is a.

User Ivan Sinigaglia
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