# Calculate the work done (in J) by a 90.0 kg man who pushes a crate 4.25 m up along a ramp that makes an angle of 20.0° with the horizontal (

Calculate the work done (in J) by a 90.0 kg man who pushes a crate 4.25 m up along a ramp that makes an angle of 20.0° with the horizontal (see below). He exerts a force of 535 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate and on his body to get up the ramp.

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W = 3.4×0³ J.

Explanation:

The work done by the man is given by the following equation:

$$W = F_{t}\cdot d$$     (1)

where W: is the work, Ft is the total force and d: is the displacement = 4.25 m.

We need to find first the total force Ft, which is:

$$Ft = Fm + W$$

where Fm: is the force exerted by the man = 535 N, W: is the weight = m*g*sin(θ), m: is the mass of the man, g: is the gravitational acceleration = 9.81 m/s², and θ: is the angle = 20.0°.

$$F_{t} = Fm + W = 500 N + 90.0 kg*9.81 m/s^{2} * sin(20.0) = 802.0 N$$

Hence, the work is:

$$W = 802.0 N \cdot 4.25 m = 3.4 \cdot 10 ^{3} J$$

Therefore, the work done by the man is 3.4×10³ J.

I hope it helps you!