Question

If the coefficient of kinetic friction between a 32 kg crate and the floor is 0.26, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if μk is zero?

a) 81.92 N; 0 N
b) 45.52 N; 5.6 N
c) 18.56 N; 10.2 N
d) 21.28 N; 3.8 N

Answer 1

The horizontal force required to move the crate at a steady speed across the floor is 81.92 N when the coefficient of kinetic friction is 0.26. However, when the coefficient of kinetic friction is zero, no horizontal force is needed to maintain the crate's steady motion.

Thus option a is correct.

Explanation:

To determine the force required to move the crate at a steady speed, use the formula:
`\(F_{\text{friction}} = \mu_k * N\)`, where N is the normal force and
`\(\mu_k\)` is the coefficient of kinetic friction. Given
`\(m = 32 \, \text{kg}\)` and
`\(\mu_k = 0.26\),` first calculate the normal force:
`\(N = m * g\) (where \(g\))` is the acceleration due to gravity, approximately 9.81 m/
`s^2`. Thus,
`\(N = 32 \, \text{kg} * 9.81 \, \text{m/s}^2 = 313.92 \, \text{N}\).` Now, find the frictional force:
`\(F_{\text{friction}} = 0.26 * 313.92 \, \text{N} = 81.92 \, \text{N}\)`.

When the coefficient of kinetic friction
`(\(\mu_k\))` is zero, the frictional force becomes
`\(0 \, \text{N}\)` since there is no resistance to motion caused by friction. Therefore, no external force is needed to maintain a steady speed.

In essence, the force required to move the crate at a steady speed across the floor is
`\(81.92 \, \text{N}\)` when the coefficient of kinetic friction is 0.26. However, when there is no kinetic friction
`(\(\mu_k = 0\))`, no horizontal force is necessary to keep the crate moving at a constant velocity as there is no opposing force due to friction. Understanding these forces helps in determining the minimum force needed to overcome friction and maintain motion or, conversely, how a lack of frictional resistance alters force requirements for motion.

Therefore option a is correct.