Question

The Mars One Landing team needs to move a large crate of mass 1500-kg on the surface of Mars. They push on the crate with a bulldozer that can only sustain a horizontal force of 3000N. The coefficients of kinetic and static friction are 0.650 and 0.720 respectivley. To help move the creat a crane is used. The astronauts attach to the top of the crate and pull straight upward on the crate with a cable.

a. What tension must the crane's steel cable (vertically) have in order for the bulldozer to move the crate (horizontally)?

b. What acceleration does the crate exerpience if the amount of tension in part (a) is applied and maintained?

Answer 1

a) acceleration due to gravity on mars = 3.73m/s²

So weight of the crate = 1500*3.73 = 5595N

Now for bulldozer to move it it needs to overcome the frictional force = u_smg = 0.720*5595= 4028.4 N

Since it can sustain only 3000N its weight in the downward direction should be

3000=0.720*W

W = 4166.67

Hence tension in the steel cable should be =5595-4166.67 = 1428.33 N

b) While moving the friction produced = u_kW = 0.650*4166.67 = 2708.3355N

So Effective force in the forward direction = 3000- 2708.3355 = 291.66N

So acceleration = a = F/m = 291.66/1500 = 0.1944 m/s²