A crate of mass m = 9.7 kg is pulled up a rough incline with an initial speed of v₁ = 1.43 m/s. The pulling force is F = 111 N parallel to the incline, which makes an angle of 19.5° with the horizontal. The coefficient of kinetic friction is 0.400, and the crate is pulled d = 5.11 m. (a) How much work is done by the gravitational force on the crate? (b) Determine the increase in internal energy of the crate-incline system owing to friction. (c) How much work is done by the 111-N force on the crate? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5.11 m? mg Part 1 of 7 - Conceptualize The gravitational force does negative work of some tens of joules on the crate. We expect some hundreds of joules of work done by the force on the crate. This force should be larger than the increase in the internal energy of the system and larger than the change in kinetic energy of the crate. We estimate the final speed to be a few meters per second.

A 24.5 kg child pulls a 3.75 kg toboggan up a hill inclined at 25.7° to the horizontal. The vertical height of the hill is 30.3 m. Friction is negligible. (a) Determine how much work the child must do on the toboggan to pull it at a constant velocity up the hill. (b) Now suppose that the hill is inclined at an angle of 19.6° but the vertical height is still 30.3 m. What conclusion can you make?

A skier of mass 71 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 40 m up a 30° slope (assumed frictionless) at a constant speed of 1.8 m/s? kJ(b) What power (expressed in hp) must a motor have to perform this task? hp

A force of constant magnitude pushes a box up a vertical surface as shown in the figure. The box moves at a constant speed. If the mass of the box is 3.70 kg, it is pushed 3.60 m vertically upward, the coefficient of friction is 0.350 and the angle ? is 30.0°, determine the following. (a) work done on the box by F J(b) work done on the box by the force of gravity J(c) work done on the box by the normal force J(d) increase in gravitational potential energy of the box as it moves up the wall J