A large globe has a radius R and a frictionless surface. A small block of mass m

Question

A large globe has a radius R and a frictionless surface. A small block of mass m slides starts from rest at the very top of the globe and slides along the surface of the globe. The block leaves the surface of the globe when it reaches a height hcrit above the ground. The geometry of the situation is shown in the figure for an arbitrary height h. Which of the following statements is true at the moment when the block leaves the surface of the globe?

a)The centripetal acceleration is zero.

b)The normal force is zero.

c)The net acceleration of the block is parallel to its velocity.

d)The kinetic energy of the block equals its potential energy.

Explanation / Answer

In the given problem

Answer is (b) The normal force is zero.

Explanation : Consider when the block is still sliding the surface but with ? > ?crit. We need to consider two forces, gravity and the normal force.

When we draw a free body diagram,lets Choose your positive x and y directions as the tangent and (inward) radial directions, respectively. Obtain the x and y components of the net force acting on the block.

Fx = mgcos(?)

Fy = mg sin(? - n)

the normal force decreases as ? becomes smaller and there is no motion in the y direction, so n = mg sin ?. As ? decreases, therefore, the normal force decreases. Therefore, when the block leaves the surface of the globe, the magnitude of the normal force becomes zero.

Then the centripetal acceleration is given by the radial component of the weight

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.