two movers have to lift a refrigerator into a truck. one of the movers wants to life the refrigerator vertically, but the other mover wants to roll it up a ramp by applying a force parallel to the ramp. assume the height of the truck is 1.5m, the length of the ramp is 5.0m, and the weight of the refrigerator is 1200.0N. calculate the force and the total work required in each case. which method is easier?

The work required is the same in both cases, and equals the potential energy increase, 1200 N * 9.8 m/s^2*1.5 m = _ J

Less force is required when the ramp is used but the movers have to push the refrigerator farther. The vertical force required would be M g. When rollers and a ramp are used, friction should be negligible. Tho force required is the component of the weights down the ramp,
M g sin A = M g (1.5/5)
where A is the ramp angle.

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To calculate the force required in each case, we can use the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

1. Lifting vertically:
In this case, the force required would be equal to the weight of the refrigerator since it is being lifted vertically against gravity. So, the force needed to lift the refrigerator vertically is 1200.0N.

2. Rolling up a ramp:
To calculate the force required to roll the refrigerator up the ramp, we need to consider the weight component parallel to the ramp. Since the ramp forms an angle with the ground, we need to find the weight component along the ramp, which can be calculated using the equation F = m * g * sin(theta), where theta is the angle formed by the ramp with the horizontal.

The angle theta can be found using trigonometry, in this case, it would be equal to the inverse sine of the height of the truck divided by the length of the ramp: theta = sin^(-1)(1.5/5.0) ≈ 17.6 degrees.

Now, we can calculate the force required to roll up the ramp: F = 1200.0 * 9.8 * sin(17.6) ≈ 341.6N.

To calculate the work required in each case, we can use the equation W = F * d, where W is the work, F is the force, and d is the distance over which the force is applied.

1. Lifting vertically:
Since the refrigerator is lifted vertically, the distance over which the force is applied is the height of the truck, which is 1.5m. So, the work required in this case would be W = 1200.0 * 1.5 = 1800.0 J (joules).

2. Rolling up a ramp:
The distance over which the force is applied is the length of the ramp, which is 5.0m. So, the work required in this case would be W = 341.6 * 5.0 = 1708.0 J (joules).

Based on the calculations, the force required to lift the refrigerator vertically is 1200.0N, while the force required to roll it up the ramp is 341.6N. The total work required to lift it vertically is 1800.0 J, and the total work required to roll it up the ramp is 1708.0 J.

Comparing the methods, rolling up the ramp requires less force but slightly more work than lifting it vertically. Therefore, in terms of energy efficiency, rolling it up the ramp is the easier method.