You are stranded on a sweltering desert island. In addition to being sweltering,

Question

You are stranded on a sweltering desert island. In addition to being sweltering, the island is sloped. Fortunately, you have found a car. What exactly you will do with it remains something of a mystery, but it is better than nothing. Because the car

You are stranded on a sweltering desert island. In addition to being sweltering, the island is sloped. Fortunately, you have found a car. What exactly you will do with it remains something of a mystery, but it is better than nothing. Because the car's brakes are broken, you have rigged a pulley system with a hanging block to hold the vehicle stationary under the only tree on the island. You need to calculate a mass for the hanging block that will keep the car stationary. If the hanging block is too heavy or too light, the car will crash into a rock or roll into the water. The mass of the car is 1210 kg and the angle of the slope from the horizontal is 6.60 degree . The rope does not stretch and the pulley is massless and frictionless. There is no friction between the car and the ground. If you have difficulty solving this, draw a free-body diagram of the forces on the car with the axes rotated so that the x axis matches the slant of the island. The entire force supplied through the rope must then equal a component of the weight.

Explanation / Answer

mass of the car (M)= 1210

mass of a block (m)

theta = 6.60

The tension forces must be made equal on each side ,so that the car will be in a stable position

Mking vertical forces equal

Mg sin(theta) = mg

m=M*sin(theta)

=1210*0.115

=139.074 kg

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