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) 0 is not the right answer.
To calculate the work done by friction, we need to use the equation:
Work = Force × Distance × Cosine(θ)
Where:
- Force is the force of friction
- Distance is the distance traveled by the block along the incline
- θ is the angle of the incline
In this case, we know the distance (15.0 m) and the angle (32.0°), but we don't know the force of friction. However, since the block is sliding at a constant velocity, we know that the net force acting on it must be zero. This means that the force of friction must be equal in magnitude and opposite in direction to the component of the gravitational force along the incline.
To find the force of friction, we need to calculate the component of the weight of the block acting along the incline:
Weight (W) = mass (m) × acceleration due to gravity (g)
In this case, the mass of the block is given as 1.11 kg. The acceleration due to gravity is approximately 9.8 m/s². Therefore:
W = 1.11 kg × 9.8 m/s²
Next, we need to find the component of the weight along the incline. This can be calculated using trigonometry:
Component of Weight along the incline (F) = Weight × sine(θ)
Finally, we can substitute the values we have into the work equation to find the work done by friction:
Work = Force × Distance × Cosine(θ)
Now let's plug in the numbers and solve:
1. Calculate the weight of the block:
W = 1.11 kg × 9.8 m/s² = 10.878 N
2. Calculate the component of weight along the incline:
F = 10.878 N × sine(32.0°)
3. Calculate the work done by friction:
Work = F × Distance × Cosine(θ)
Substitute the values:
Work = (10.878 N × sine(32.0°)) × 15.0 m × Cosine(32.0°)
Use a calculator to evaluate the trigonometric functions and perform the multiplication to find the work done by friction.