A block on a horizontal surface is moving with velocity and there is a kinetic friction μ_k N opposing motion. What is the direction of work done by friction?

A block on a horizontal surface is moving with velocity and there is a kinetic friction μ_k N opposing motion. What is the direction of work done by friction?

• A. Friction does positive work
• B. Friction does negative work
• C. Friction does zero work
• D. Work by friction depends on velocity

Answer: (B)

When a block slides on a horizontal surface, the kinetic friction force points opposite to the direction the block is moving. Work is defined as F · d, the force times displacement, with the angle between force and displacement determining the sign via cos(theta). Since friction is directly opposite the motion, the angle is 180 degrees, so cos(theta) is -1. The work done by friction is negative: W_friction = - μ_k N d (the magnitude μ_k N times the displacement d). On a horizontal surface, N is mg, so W_friction = - μ_k m g d. This negative work means friction removes energy from the block (it converts some of the kinetic energy into heat at the contact). The speed or velocity magnitude doesn’t change the sign—it's the opposite direction to the motion that makes the work negative. If there were no displacement, or the block were at rest with static friction, the work would be zero.

When a block slides on a horizontal surface, the kinetic friction force points opposite to the direction the block is moving. Work is defined as F · d, the force times displacement, with the angle between force and displacement determining the sign via cos(theta). Since friction is directly opposite the motion, the angle is 180 degrees, so cos(theta) is -1. The work done by friction is negative: W_friction = - μ_k N d (the magnitude μ_k N times the displacement d). On a horizontal surface, N is mg, so W_friction = - μ_k m g d. This negative work means friction removes energy from the block (it converts some of the kinetic energy into heat at the contact). The speed or velocity magnitude doesn’t change the sign—it's the opposite direction to the motion that makes the work negative. If there were no displacement, or the block were at rest with static friction, the work would be zero.