Final answer:
To find the work done by Pete in raising the crate, we would typically use the formula for work against gravity, which is W = mgh. The mass of the crate is needed, which is not provided, so we cannot calculate the exact amount of work done. Without the mass, we can't account for the work done against friction either.
Step-by-step explanation:
To calculate the work done by Pete when raising a crate a vertical distance of 2.7 m up a ramp at a constant speed, we need to understand work is the product of the force applied in the direction of displacement and the displacement itself. Since the crate moves at a constant speed, the net force acting on it is zero, which means the force Pete applies also overcomes the force of friction. The ramp angle and the coefficient of friction are provided to understand the scenario better, but the vertical distance allows us to find the work done by Pete without needing to decompose the forces.
To start, let's recall the work done is related to the height raised and the weight (mg) of the object because the force applied by Pete must be equal to the component of the weight of the crate parallel to the ramp plus the force of friction. However, we lack the mass of the crate to determine its weight and consequently the friction force. Nevertheless, we can use the vertical height and gravitational force to find the minimum work done by Pete, assuming he is exerting a force just enough to counteract gravity and any friction force for the crate to ascend at a constant speed.
The work done (W) to lift the crate vertically can be calculated using the equation:
W = Fparallel × d, where Fparallel is the component of Pete's force that is parallel to the displacement up the ramp and d is the displacement along the ramp. With the given vertical distance (h) and the angle (θ) of the ramp, we can find the displacement along the ramp using trigonometry: d = h / sin(θ). However, the actual work done includes overcoming both gravity and friction, and since the coefficient of friction (u) is given but the mass is unknown, we will focus on the gravity part. The work done against gravity is W = mgh. We need the weight of the crate for this calculation, which we do not have. Therefore, with given information, we cannot provide an exact value for the work done.