I need help with these two.
1. A horizontal force pulls a 20-kg box across the floor with constant speed. μs is 0.60, how much work does F do in moving the cart 3.0 m?
2. A 400 lb load of bricks is to be lifted to the top of a scaffold 30 feet high. How much work to lift it?
1. if μs is static coefficent, it wont help here, you need μk
work= μk*20*g*3
2. work=mgh
here, mg=400 lbs
work=400*30 ft-lbs
To solve the first question, we can use the equation for work:
Work = Force × Distance × cos(θ)
In this case, the force F is pulling the box horizontally, so the angle θ between the force and the displacement is 0 degrees (cos(0) = 1).
We are given the mass of the box, which is 20 kg, and the coefficient of static friction, μs, which is 0.60. Since the box is moving with constant speed, the static friction force is equal to the applied force F.
Using the equation F = μs × Normal force, we can find the normal force acting on the box. The normal force is equal to the weight of the box, which is mass × acceleration due to gravity. Using a typical value of 9.8 m/s^2 for the acceleration due to gravity, we have:
Normal force = 20 kg × 9.8 m/s^2 = 196 N
Now, we can calculate the force F:
F = μs × Normal force = 0.60 × 196 N = 117.6 N
Finally, we can calculate the work done by F in moving the box:
Work = F × Distance × cos(θ) = 117.6 N × 3.0 m × cos(0) = 352.8 Joules
Therefore, the work done by the force F in moving the box 3.0 m is 352.8 Joules.
Moving on to the second question, we can use a similar approach to solve for the work.
Work = Force × Distance × cos(θ)
In this case, we need to calculate the force required to lift the load of bricks. The force needed to lift an object can be determined using the equation:
Force = Mass × acceleration due to gravity
Note that the mass is given in pounds in the question, so we need to convert it to kilograms using the conversion factor of 1 lb = 0.4536 kg.
Mass = 400 lb × 0.4536 kg/lb = 181.44 kg
The acceleration due to gravity is 9.8 m/s^2.
Force = 181.44 kg × 9.8 m/s^2 = 1777.59 N
Now, we can calculate the work done to lift the load of bricks:
Work = Force × Distance × cos(θ)
The distance is given as 30 feet, which we need to convert to meters using the conversion factor of 1 ft = 0.3048 m.
Distance = 30 ft × 0.3048 m/ft = 9.144 m
Since the load is being lifted vertically, the angle θ between the force and the displacement is 0 degrees (cos(0) = 1).
Work = 1777.59 N × 9.144 m × cos(0) = 16208.07 Joules
Therefore, the work required to lift the load of bricks to the top of the scaffold is 16208.07 Joules.