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a grocery cart with mass of 16 kg is being pushed at constant speed up a 12° ramp by a force f which acts at an angle of 17 below the horizontal. find the work done by each of the forces (mg, fn, fp) on the cart if the ramp is 7.5 m long.

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Final answer:

The work done by each of the forces on the cart can be found using the formulas for work and the given information about the forces. The work done by the frictional force and the gravitational force can be calculated using the formulas for work, while the work done by the shopper can be calculated using the formula for work and the given angle of the applied force. The force exerted by the shopper can be calculated using the formula for force and the given mass and acceleration.

Step-by-step explanation:

The work done by each of the forces on the cart can be found using the formula:

Work = Force x Distance x Cos(θ)

(a) The work done by the frictional force is given by:

Work_friction = frictional force x distance x Cos(180°)

Since the cart is moving at constant speed on level ground, the work done by the frictional force is zero.

(b) The work done by the gravitational force can be found using the formula:

Work_gravitational = weight x distance x Cos(θ)

Weight = mass x gravity, and in this case, the angle θ is 0° since the cart is on level ground. So:

Work_gravitational = mass x gravity x distance x Cos(0°)

(c) The work done by the shopper can be found using the formula:

Work_shopper = applied force x distance x Cos(θ_shopper)

(d) The force the shopper exerts can be found using the formula:

Force_shopper = mass x acceleration_shopper

(e) The total work done on the cart is the sum of the work done by all the forces.

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