A 1.11 kg block slides down a 15.0 m long 32.0° incline at constant velocity. How much work is done by friction?
(please help me show me how to solve using equation and where to plug the numbers)
To find the work done by friction, we can use the equation:
Work = Force × Distance × cos(θ)
Where:
- Force is the force of friction,
- Distance is the distance traveled by the block, and
- θ is the angle between the direction of the force and the direction of motion.
In this problem, we are given:
- The mass of the block is 1.11 kg.
- The distance traveled by the block is 15.0 m.
- The angle of the incline is 32.0°.
To find the force of friction, we need to decompose the weight of the block into two components: one parallel to the incline and the other perpendicular to it.
The weight of the object (mg) can be broken down as follows:
- Parallel component (mg sinθ): This force component acts down the incline.
- Perpendicular component (mg cosθ): This force component acts perpendicular to the incline.
Noting that the block slides down the incline at a constant velocity, it means that the force of friction must be equal in magnitude and opposite in direction to the parallel component of the weight. So:
Force of friction = mg sinθ
Now we can calculate the work done by friction:
Work = (mg sinθ) × distance × cos(θ)
Let's plug in the numbers:
Mass (m) = 1.11 kg
Acceleration due to gravity (g) = 9.8 m/s²
Distance (distance) = 15.0 m
Angle (θ) = 32.0°
Plugging these values into the equation:
Work = (1.11 kg * 9.8 m/s² * sin(32.0°)) * 15.0 m * cos(32.0°)
Now, calculate the sin(32.0°) and cos(32.0°) using a calculator, then substitute these values into the equation and solve it to find the work done by friction.