Block in the Car?

Question

A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 34 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 155 m), the block swings toward the outside of the curve. Then the string makes an angle with the vertical. Find the angle.

How does the force compare with the block? is the radius if the circle proportional to the radius of the blocks circle?

Answer 1

F=ma, and
a=v^/r

Therefore, F=mv^2/r
=m*34^2/155
=7.45m N

There are 3 forces acting on the string, the weight mg of the block in the downward direction, the centripetal force, F which we have just computed to be equal to 7.45m N, and the tension T in the string. If you draw a diagram showing this 3 forces, you will find that the angle from the vertical made by the string is equal arctanF/mg, i.e. tantheta=7.45m/mg
=7.45/9.8
=0.760

Use a scientific calculator to get the angle.

The centripetal force on the van will be proportional to the centripetal force on the block, and the angle theta will be the same as the angle of the banked curve if it were to be banked. Likewise the radius of the circle will be proportional to that of the
block. The reason for this is that the velocity of the van is the same as the velocity of the block. Thus the terms in the formula F=mv^2/r for the van will be in direct proportion to those of the block, if we compare them with one another.