Answer:
To calculate the force required to push the box up the ramp, we first need to determine the normal force (N) acting on the box, which is the force perpendicular to the ramp. The normal force is equal to the weight of the box, which is:
N = m*g
N = 100 kg * 9.8 m/s^2
N = 980 N
where m is the mass of the box and g is the acceleration due to gravity.
Next, we can calculate the force of static friction (Fs) acting on the box, which is the force that opposes the box from sliding down the ramp. The maximum force of static friction is given by:
Fs = μs*N
Fs = 0.9 * 980 N
Fs = 882 N
where μs is the coefficient of static friction.
Since the pushing force is limited to 1000 N, the box will not start sliding down the ramp due to static friction. Thus, we can use the maximum force of static friction to calculate the force required to push the box up the ramp. The force required to push the box up the ramp is given by:
F = mgsin(θ) + Fs*cos(θ)
F = 100 kg * 9.8 m/s^2 * sin(20°) + 882 N * cos(20°)
F = 344.7 N + 832.8 N
F = 1177.5 N
where θ is the angle of the ramp with the horizontal, which is 20 degrees in this case, and μk is the coefficient of kinetic friction.
Since the pushing force available is only 1000 N, it is not sufficient to push the box up the ramp. Therefore, additional force or help is needed to move the box into the truck.