How much work would it take to push a # 5 kg # weight up a # 4 m # plane that is at an incline of # pi / 4 #?

Question

How much work would it take to push a #   5  kg  # weight up a #  4   m # plane that is at an incline of #  pi  /  4 #?

Nora Arzate · Accepted Answer

The explanation below includes two possible approaches to this calculation. The answer (in some ways the least interesting bit!) is #138.6 J#.

The solution to this problem can be computed in at least two different ways. The first uses the formula #W = Fd#, that is, work = force * distance The distance traveled up the slope will be #4 m#. The required force will be the component of the gravitational force on the object in the direction of motion, #F = mg sin theta = 5*9.8 sin (pi/4) = 34.5N# #W=f*d = 34.5*4 =138.6 J# In the second, the object's energy is changed by work; in this example, sliding the object up the ramp raises its height and, consequently, its gravitational potential energy. #E_p=mgh# where #m# is the mass #(kg)#, #g# is the acceleration due to gravity, #9.8 ms^-2# and #h# is the height #(m)#. Trigonometry and the definition of sine are used in the calculation of the height: #h=4*sin(pi/4) = 2.83 m# #E_p=mgh = 5*9.8*2.83 = 138.6 J# (actually 138.7 on these numbers due to rounding issues)

Benjamin Asiedu · Answer

undefined To calculate the work done, you can use the formula: Work = Force × Distance × Cosine(angle). Given that the weight is 5 kg and the incline angle is π/4 radians (45 degrees), the force required can be calculated using the weight and the angle. The force required is equal to the weight times the sine of the angle. Then, you can calculate the work using the given distance and the calculated force.