1) weight of the box: 980 N
The weight of the box is given by:
\(W=mg\)
where m=100.0 kg is the mass of the box, and \(g=9.8 m/s^2\) is the acceleration due to gravity. Substituting in the formula, we find
\(W=(100.0 kg)(9.8 m/s^2)=980 N\)
2) Normal force: 630 N
The magnitude of the normal force is equal to the component of the weight which is perpendicular to the ramp, which is given by
\(N=W cos \theta\)
where W is the weight of the box, calculated in the previous step, and \(\theta=50^{\circ}\) is the angle of the ramp. Substituting, we find
\(N=(980 N)(cos 50^{\circ})=630 N\)
3) Acceleration: \(7.5 m/s^2\)
The acceleration of the box along the ramp is equal to the component of the acceleration of gravity parallel to the ramp, which is given by
\(a_p = g sin \theta\)
Substituting, we find
\(W_p = (9.8 m/s^2)(sin 50^{\circ})=7.5 m/s^2\)
