Calculating Forces and Weight of a Mass on a Plank

[cosmokramer]

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A uniform plank has a mass of Mp = 4.84 kilograms. Upon it sits a box with mass = 19.66 kilograms. If the left end of the plank is taken to be x=0, then x1, the location of the first saw horse, is 2.27 m, x2, the location of the second saw horse is, 6.27 m and the box is located at x3 = 4.53 m. The plank is 7.32 meters long.

a) What is the force applied by the right most saw horse on the plank?

b) What is the force applied by the left saw horse on the plank?

c) What is the sum of the forces applied by the saw horses on the plank?

d) What is the net weight of the block and plank?

 

[Integral]

Please demonstrate that you have put some thought into this problem.

 

[wais]

a) The force applied by the right most saw horse on the plank can be calculated using the formula F = (Mp + Mb)g, where Mp is the mass of the plank, Mb is the mass of the box, and g is the acceleration due to gravity (9.8 m/s^2). Plugging in the values, we get F = (4.84 kg + 19.66 kg)(9.8 m/s^2) = 240.4 N. Therefore, the force applied by the right most saw horse on the plank is 240.4 Newtons.

b) Similarly, the force applied by the left saw horse on the plank can be calculated using the same formula, F = (Mp + Mb)g. However, the mass of the box needs to be subtracted from the total mass, as it is located on the left side of the plank. Therefore, the force applied by the left saw horse on the plank is (4.84 kg + 19.66 kg - 19.66 kg)(9.8 m/s^2) = 48.4 N.

c) The sum of the forces applied by the saw horses on the plank can be calculated by adding the forces from both the left and right saw horses. Therefore, the sum of the forces is 240.4 N + 48.4 N = 288.8 N.

d) The net weight of the block and plank can be calculated by adding the weight of the plank and the weight of the box. The weight of the plank can be calculated using the formula W = Mg, where M is the mass of the plank and g is the acceleration due to gravity. Therefore, the weight of the plank is (4.84 kg)(9.8 m/s^2) = 47.4 N. The weight of the box is (19.66 kg)(9.8 m/s^2) = 192.8 N. The net weight of the block and plank is 47.4 N + 192.8 N = 240.2 N.