Answer: When a crate slides down a ramp at a constant speed, it means that the net force acting on the crate is zero. In this case, the force of gravity acting downward is balanced by the force of friction acting upward along the ramp. The work done by friction in this scenario converts mechanical energy into thermal energy, resulting in an increase in thermal energy.
To calculate the amount of thermal energy created, we need to determine the work done by friction. The work done by friction can be calculated using the formula:
Work = Force × Distance × Cosine of the angle between the force and the displacement
In this case, the force of friction is equal to the force of gravity component parallel to the ramp, which can be calculated as:
Force of gravity parallel to the ramp = Weight of the crate × Sin(θ)
where θ is the angle of the ramp (31°) and the weight of the crate is equal to its mass multiplied by the acceleration due to gravity.
Weight of the crate = mass × acceleration due to gravity
Once we calculate the force of friction, we can then determine the work done by friction using the given distance (12 m).
The thermal energy created is equal to the work done by friction. Remember that work and energy are measured in the same units (joules).
Let's calculate the thermal energy created step-by-step:
Calculate the weight of the crate:
Weight of the crate = mass × acceleration due to gravity
Calculate the force of gravity parallel to the ramp:
Force of gravity parallel to the ramp = Weight of the crate × Sin(θ)
Calculate the work done by friction:
Work = Force of friction × Distance × Cos(θ)
The thermal energy created is equal to the work done by friction.
Please provide the mass of the crate, and I can help you calculate the thermal energy created.