A 1.15 kg block slides down a 19.0 m long 29.0° incline at constant velocity. How much work is done by friction?
Friction does negative work. Since there is no acceleration, the friction work equals the potential energy loss.
The incline angle does no matter in this case.
To find the work done by friction, we need to know the force of friction and the distance over which it acts.
To determine the force of friction, we can use the fact that the block is sliding down the incline at a constant velocity. At constant velocity, the net force acting on the block is zero. The weight of the block can be resolved into two components: one parallel to the incline (mg*sinθ) and one perpendicular to the incline (mg*cosθ), where m is the mass of the block and θ is the angle of the incline.
Since the block is moving at a constant velocity, the force of friction must be equal and opposite to the component of the weight parallel to the incline. Therefore, the force of friction is equal to mg*sinθ.
To calculate the work done by friction, we can use the equation:
Work = Force × Distance × cosφ
where Force is the force of friction, Distance is the length of the incline, and φ is the angle between the force and the direction of motion.
In this case, the force of friction is mg*sinθ, the distance is 19.0 m, and the angle between the force and the direction of motion is 180° (since the force of friction is opposite to the direction of motion). Therefore, φ = 180°.
Plugging in these values, we get:
Work = (mg*sinθ) × Distance × cos(180°)
= (1.15 kg × 9.8 m/s^2) × sin(29.0°) × 19.0 m × cos(180°)
Calculating this expression will give us the work done by friction.