Math  /  Algebra

Question(II) A grocery cart with mass of 16 kg is pushed at constant speed up a 1212^{\circ} ramp by a force FPF_{\mathrm{P}} which acts at an angle of 1717^{\circ} below the horizontal. Find the work done by each of the forces (mgundefined,FundefinedN,FundefinedP)\left(m \overrightarrow{\mathbf{g}}, \overrightarrow{\mathbf{F}}_{\mathrm{N}}, \overrightarrow{\mathbf{F}}_{\mathrm{P}}\right) on the cart if the ramp is 7.5 m long.

Studdy Solution
Calculate the work done by the applied force FPF_{\mathrm{P}}.
The component of the applied force along the ramp is FPcos(17+12)F_{\mathrm{P}} \cos(17^{\circ} + 12^{\circ}).
Since the cart moves at constant speed, the net work done is zero, so the work done by the applied force must balance the work done by gravity:
Wapplied=Wgravity W_{\mathrm{applied}} = -W_{\mathrm{gravity}}
Thus, the work done by the applied force is equal in magnitude but opposite in sign to the work done by gravity.
The work done by each of the forces is: - Gravitational force: Wgravity W_{\mathrm{gravity}} - Normal force: Wnormal=0 W_{\mathrm{normal}} = 0 - Applied force: Wapplied=Wgravity W_{\mathrm{applied}} = -W_{\mathrm{gravity}}

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