A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 27.8 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 196 m), the block swings toward the outside of the curve. Then the string makes an angle è with the vertical. Find è.
hey damon, thats not what she asked
(27.8^2)/(196*9.8)=x
arctanx= answer
To find the angle è, we need to analyze the forces acting on the block when the van is moving around the unbanked curve.
First, let's consider the forces acting on the block when the van is moving straight ahead. In this case, the only force acting on the block is the tension force in the string, which is equal to the weight of the block, since it hangs vertically down. The tension force can be calculated using the equation:
Tension force = mass of the block * acceleration due to gravity
Now, when the van is moving around the unbanked curve, there are two additional forces acting on the block. The first one is the tension force in the string, which still points vertically upward. The second force is the horizontal component of the normal force exerted by the van on the block, which points towards the center of the curve. This horizontal component provides the centripetal force necessary to keep the block moving in a circle.
Since the block is not accelerating vertically, the tension force in the string must cancel out the vertical component of the weight of the block. This can be expressed as:
Vertical component of tension force = mass of the block * acceleration due to gravity
Furthermore, the horizontal component of the normal force provides the centripetal force required to keep the block moving in a circle. This can be expressed as:
Horizontal component of normal force = mass of the block * centripetal acceleration
The centripetal acceleration can be calculated using the equation:
Centripetal acceleration = (velocity of the van)^2 / radius of the curve
Now, to find the angle è, we can use trigonometry. The tangent of the angle è is given by:
tan(è) = (horizontal component of normal force) / (vertical component of tension force)
Substituting the values we've obtained:
tan(è) = (mass of the block * centripetal acceleration) / (mass of the block * acceleration due to gravity)
Simplifying:
tan(è) = centripetal acceleration / acceleration due to gravity
Finally, we can substitute the expression for centripetal acceleration and acceleration due to gravity:
tan(è) = ((velocity of the van)^2 / radius of the curve) / acceleration due to gravity
tan(è) = (27.8 m/s)^2 / (196 m) / (9.8 m/s^2)
Evaluating this expression will give us the value of tan(è). By taking the inverse tangent, we can find the angle è.
tan e = (m v^2 /r) /mg = v^2/rg
Hey Gina, you better read that chapter on centripedal acceleration carefully. All your questions are really the same.