To calculate the work done against friction, we need to determine the change in kinetic energy of the mass as it slides down the incline plane. The work done against friction is equal to the negative of this change in kinetic energy.
Given: Mass (m) = 5 kg Length of incline (s) = 30 m Angle of incline (θ) = 30° Final velocity (v) = 26 m/s
To calculate the work done against friction, we'll follow these steps:
Calculate the initial velocity (u): Since the mass starts from rest, the initial velocity (u) is 0 m/s.
Calculate the change in height (Δh): The vertical height (h) can be calculated using the formula: h = s * sin(θ) Δh = h = s * sin(θ) = 30 m * sin(30°) = 15 m
Calculate the change in potential energy (ΔPE): The change in potential energy is given by: ΔPE = m * g * Δh where g is the acceleration due to gravity (approximately 9.8 m/s²): ΔPE = 5 kg * 9.8 m/s² * 15 m = 735 J
Calculate the change in kinetic energy (ΔKE): The change in kinetic energy is given by: ΔKE = 0.5 * m * (v² - u²) ΔKE = 0.5 * 5 kg * ((26 m/s)² - (0 m/s)²) = 0.5 * 5 kg * (676 m²/s²) = 1690 J
Calculate the work done against friction (W_friction): The work done against friction is the negative of the change in kinetic energy: W_friction = -ΔKE = -1690 J
Therefore, the work done against friction is -1690 Joules. Note that the negative sign indicates that work is done against the motion due to the opposing frictional force.